PUBLICACIONES
                                                                                            
RAFAEL  D. BENGURIA



Ph.D. Thesis:
The von Weizsäcker and exchange corrections in the Thomas Fermi theory,
Princeton University, Princeton, NJ, 1979



151. R. D. Benguria and M.C. Depassier, Speed of spreading fronts of the reaction diffusion equation with Stefan boundary conditions,  arXiv:1910.11695 (2019).

150. R. D. Benguria and S. Benguria, A Non-Existence Result for a Generalized Radial Brezis-Nirenberg Problem, submitted (2019).

149. R. D. Benguria, C. Vallejos, and H. Van Den Bosch, Existence and nonexistence of minimizers for Poincaré-Sobolev Inequalities, accepted for publications in Calculus of Variations (2019).

148. R. D. Benguria, B. Brandolini, and F. Chiacchio, A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere, accepted for publication in Communications in Cotnemporary Mathematics (2019), published online: https://doi.org/10.1142/S0219199719500184

147. R. D. Benguria, and A. Solar, An Estimation of Level Sets for Non Local KPP Equations with Delay, Nonlinearity 32, 777-799 (2019).

146. R. D. Benguria, and A. Solar, An iterative estimation for disturbances of semi-wavefronts to the delayed Fisher-KPP equation, Proceedings  of the American  Mathematical  Society  147, 2495-2501 (2019).

145. R. D. Benguria, C. Vallejos, and H. Van Den Bosch, Gagliardo-Nirenberg-Sobolev Inequalities for Convex Domains in Rd, accepted for publication in Mathematics Research Letters, to appear in volume 26 (2019).

144. R. D. Benguria, M. C. Depassier, Variational Characterization of the Speed of Reaction Diffusion Fronts for Gradient Dependent Diffusion,  Annales Henri Poincaré 19, 2717-2726 (2018).

143. R. D. Benguria and S. Benguria, The Brezis-Nirenberg problem for the Laplacian with a singular drift in Rnand Sn.,
Nonlinear Analysis, Theory, Methods and Applications, 157, 189-2011 (2017).

142. R. D. Benguria, S. Fournais, E. Stockmeyer, and H. Van Den Bosch, Spectral gaps of Dirac operators describing Dirac quantum dots,  Mathematical Physics Analysis and Geometry 20, article 11, (2017).

141. R. D. Benguria, S. Fournais, E. Stockmeyer, and H. Van Den Bosch,  Self-Adjointness of Two Dimensional Dirac Operators on Domains, Annales Henri Poincaré, 18,  1371-1383  (2017).

140. R. D. Benguria, and S. Benguria, An improved bound for the non-existence of radial solutions of the Brezis-Nirenberg problem in Hn, in Functional Analysis and Operator Theory for Quantum Physics, A Festschrift in Honor of Pavel Exner, J. Dittrich, H. Kovarik, A. Laptev (Eds.), Europ. Math. Soc. Publ. House, 2017, pp. 153-160.  

139. R. D. Benguria, M. C. Depassier, and M. Loss, Monotonicity of the period of a non linear oscillator, Nonlinear Analysis, Theory, Methods and Applications, 140, 61–68 (2016).

138. R. D. Benguria and M. C. Depassier, Reaction diffusion dynamics and the Schryer-Walker solution for domain walls of the Landau-Lifshitz-Gilbert equation, Physical Review B 93, 144416 (2016).

137. R. D. Benguria, Maxwell 150: a celebration in the International Year of Light, International Association of Mathematical Physics, News Bulletin, October 2015 issue, pp. 19-33.

136. R. D. Benguria,
Density Functional Theory, in Encyclopedia of Applied and Computational Mathematics,
Editor-in-chief: Engquist, Bj\"orn,
Chan, T.; Cook, W.J.; Hairer, E.; Hastad, J.; Iserles, A.; Langtangen, H.P.; Le Bris, C.; Lions, P.L.; Lubich, C.; Majda, A.J.; McLaughlin, J.; Nieminen, R.; Oden, J.T.; Souganidis, P.; Tveito, A. (Eds.), Springer--Verlag, Berlin., pp. 345-351 (2015)

135. R. D. Benguria, and H. Van Den Bosch, A criterion for the existence of zero modes for the Pauli
operator with fastly decaying fields, J. Math. Phys. 56, 052104 (2015).

134. R. D. Benguria, R. L. Frank, and E. H. Lieb,
Ground state energy of large polaron systems, J. Math. Phys. 56, 021901 (2015).

133. R. D. Benguria, The centenary of Mark Kac (1914--1984), International Association of Mathematical Physics,
News Bulletin, July 2014 issue, pp. 5-18.

132.  R. D. Benguria, M. C. Depassier, Shift in the speed of reaction--diffusion equation with a cut--off: Pushed and bistable fronts, Physica D (Nonlinear Phenomena), 280--281, 38-43 (2014).

131. R. D. Benguria, and B. Loewe, Stability of Matter, in Complex Quantum Systems: Analysis of Large Coulomb Systems,
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 24, Heinz Siedentop, Editor,
pp. 1-60, Singapore, 2013.

130. R. D. Benguria, Stabiliy of Matter, in Operator Theory Advances and Applications224 , 25-54 (2012).

129. Rafael Benguria, Eduardo Friedman, Marius Mantoiu, Editors,
Spectral Analysis of Quantum Hamiltonians,
Spectral Days 2010, Birkhäuser, Basel, 2012. [Book]

128. R. D. Benguria,  and Matej Tusek,
Indirect Coulomb energy for two-dimensional atoms
, J. Math. Phys. 53, 095213 (2012).

127. R. D. Benguria,
A Centennial of Rutherford's Atom,
International Association of Mathematical Physics (IAMP) News Bulletin, pp. 4-10, January, 2012.

126. R. D. Benguria, G.A. Bley,
Improved Results on the No-binding of Bipolarons,
J. Phys. A: Math. Theor. 45, 045205 (2012).

125. R. D. Benguria, P. Gallegos, and Matej Tusek,
A New Estimate on the Two-Dimensional Indirect Coulomb Energy,
Annales Henri Poincaré 13, 1733-1744 (2012).

124. R. D. Benguria, M. C. Depassier, and M. Loss, 
Rigorous results for the minimal speed of Kolmogorov--Petrovskii--Piscounov monotonic fronts with a cutoff
,
J. Math. Phys.  53, 123705 (2012).

123. R. D. Benguria, H. Linde, and B. Loewe,
Isoperimetric Inequalities for Eigenvalues of the Laplacian and the Schrödinger Operator,
Bulletin of Mathematical Sciences 2, 1--56 (2012).

122. R.D. Benguria,  G. A. Bley,  and M. Loss, 
A new estimate on the indirect Coulomb energy
,
International Journal of Quantum Chemistry 112, 1579-1584 (2012).

121. R. D. Benguria,
Los Átomos: La Fantástica Historia de su Descubrimiento, en
Temporalidad, Interacción y Dinamismo Cultural: La búsqueda del hombre; homenaje al Profesor Dr. Lautaro Núñez Atencio, A. Hubert, J. A. González, M. Pereira (Eds.), pp. 503-515, Universidad Católica del Norte, Ediciones Universitarias, Antofagasta, 2011.

120. R. D. Benguria,
Isoperimetric Inequalities for Eigenvalues of the Laplacian,
in Isoperimetric inequalities, Random Matrices, Boltzmann's equation, and Random Schrödinger operators,
Proceedings of the Arizona School of Analysis with Applications
University of Arizona, Tucson, Monday 15 - Friday 19 March 2010, (R. Sims, and D. Ueltschi, Eds.),
Contemporary Mathematics 552, 21-60 (2011).
 
119.  R.D. Benguria y G. A.  Bley,
Exact Asymptotic Behavior of the Pekar-Tomasevich Functional,  
Journal of Mathematical Physics 52, 052110 (7) (2011)

118.  R. D. Benguria,
Spectral Problems in Spaces of Constant Curvature,
in Mathematical Results in Quantum Physics:
Proceedings of the QMath11 Conference, held in Hradec Kralove, September 2010,
P. Exner, Ed., pp. 131--137,
World Scientific, Singapore, 2011.
 
117. M. S. Ashbaugh, and R. D. Benguria,
El problema de la Reina Dido: Panorama sobre los problemas de la isoperimetría
,
El Joven Matemático, número 1, pp. 3--8 (2010). [English translation][French translation (by J. Fleckinger-Pellé)].

116.  M. Beau, R.D. Benguria, R. Brummelhuis, and P. Duclos, 
H2 molecule in strong magnetic fields,
J. Phys. A: Math & Theor. 43, Art. 474005 (2010).

115.  R.D. Benguria,  C. Fernández, P. Duclos, and C. Sing-Long,
A nonlinear ordinary differential equation associated with the quantum sojourn time

J. Phys. A: Math & Theor. 43, Art. 474007 (2010).

114.  R. Benguria, M. Levitin, and L. Parnovski,
Fourier transform, null variety, and Laplacian's eigenvalues,
Journal of Functional Analysis, 257, 2088--2123 (2009)

113.  R. Benguria, J. Dolbeault, and R. Monneau,
Harnack Inequalities and Discrete-Continuous Error Estimates for a Chain of Atoms with Two-Body Interactions

Journal of Statistical Physics 134, 27--51 (2009).

112. R.D. Benguria and  H. Linde,
Isoperimetric Inequalities for Eigenvalues of the Laplace Operator
,
in Fourth Summer School in Analysis and Mathematical Physics: Topics in Spectral Theory and Quantum Mechanics,
May 2005, Universidad Nacional Autónoma de México, Inst. Math. Phys, Cuernavaca, México,
Contemporary Mathematics 476, 1-40 (2008)

111.  R.D. Benguria, M.C. Depassier, and M. Loss,
Upper and lower bounds for the speed of pulled fronts with a cut-off
,
European Physical Journal B 61, 331--334 (2008).

110. R. D. Benguria, M. Loss, and H. Siedentop,
Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsäcker model

Journal of Mathematical Physics 49, 012302 (7) (2008).

109. R. D. Benguria, R. Frank, and M. Loss,
The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three dimensional upper half plane
,
Mathematical Research Letters, 15, 613-622 (2008).

108. R. D. Benguria, M. C. Depassier, V. Haikala,
The effect of a cutoff on pushed and bistable fronts of the reaction difusion equation
,
Physical Review E 76, 051101 (3)  (2007).

107. R.D. Benguria, and H. Linde, 
A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space,
Duke Mathematical Journal  140,  245-279 (2007).

106. A. Reisenegger, R. Benguria, J. P. Prieto, P. A. Araya, and D. Lai,
Hall drift of axisymmetric magnetic fields in solid neutro-star matter
,
Astronomy and Astrophysics, 472, 233-240 (2007).

105. M. S. Ashbaugh, y R. D.  Benguria,
Isoperimetric Inequalities for Eigenvalues of the Laplacian,
in Spectral Theory and Mathematical Physics:  A Festschrift in Honor of Barry Simon's 60th Birthday,
(F. Gesztesy, P. Deift, C. Galvez, P. Perry, and W. Schlag, Eds.)
Proceedings of Symposia in Pure Mathematics  76, Part 1, pp. 105-139, Amer. Math. Soc. (Providence, RI) 2007.

104. R. D. Benguria, and M. C. Depassier,
Speed of pulled fronts with a cutoff
,
Physical Review E 75, 051106 (5) (2007).

103. R.D. Benguria, and H. Linde, 
A second eigenvalue bound for the Dirichlet Schrödinger operator
,
Communications in Mathematical Physics 267, 741-755 (2006).

102. R. D. Benguria,
A nonlinear fourth-order minimization problem
,
Contemporary Mathematics 412, 79-86 (2006).

101. R. D. Benguria, R. Brummelhuis, P. Duclos, S. Pérez-Oyarzún, y P. Vytras,
Asymptotic behaviour of the equilibrium nuclear separation for the H2+ molecule in a strong magnetic field,
Journal of  Physics A: Mathematical and  General  39, 8451 - 8459 (2006).

100. R. D. Benguria, R. Brummelhuis, P. Duclos, S. Pérez-Oyarzún, and P. Vytras,
Non-relativistic
H2+ molecule in a strong magnetic  field
Few Body Systems 38, 133-137 (2006).

99. A. Reisenegger, J. Prieto, R. D. Benguria, Dong Lai, P. Araya,
Magnetic Field in Neutron Stars: A Theoretical Perspective,
in Magnetic Fields in the Universe:  from Laboratory and Stars to Primordial Structures,
Angra dos Reis, Brazil, Nov 28 - Dec 3, 2004, (E. M. de Gouveia dal Pino, A. Lazarian, & G. Lugones, Eds.),
AIP Conference Proceedings 784, pp. 263-273 (2005).

98.  R. D. Benguria, and M. Cristina Depassier,
On the transition from pulled to pushed monotonic fronts of the extended Fisher-Kolmogorov equation
,
Physica A  356, 61-65 (2005).

97. T. Andrade, M. Bañados , R.D. Benguria, and A. Gomberoff, 
(2+1)-Dimensional Charged Black Hole in Topologically Massive Electrodynamics
,
Physical Review Letters 95,  021102 (4) (2005).

96. R.D. Benguria, and M. Cristina Depassier,
On the principal bifurcation branch of a third-order nonlinear long-wave equation
Journal of  Physics A: Mathematical and  General  38, 2043-2053 (2005).

95. R.D. Benguria, and M. C. Depassier,
Variational Principles for the Speed of Traveling Fronts of Reaction-Diffusion Equations
,
in Variational and Extremum Principles in Macroscopic Systems, (S. Sieniutycz, Ed.),
Elsevier Science, pp. 339-352 (2005).

94. J. Asch, R.D. Benguria, and P. Stovicek, 
Asymptotic properties of the differential equation h3(h"+h')=1

Asymptotic Analysis   41, 23- 40 (2005). 

93. R.D. Benguria and S. Wugalter,
Bounding threshold for the Pauli--Fierz operator,
Letters in Mathematical Physics 70, 249 - 257 (2004).

92. R. D. Benguria, I. Catto, J. Dolbeault and R. Monneau,  
Oscillating minimizers of a fourth order problem invariant under scaling

Journal of Differential Equations, 205, 253-269 (2004).

91. R. D. Benguria, and Michael Loss,
Connection between the Lieb--Thirring conjecture for Schrödinger operators and an isoperimetric problem for ovals on the plane
, in Partial Differential Equations and Inverse Problems, C.  Conca, R. Manásevich, G. Uhlmann, and M.S. Vogelius (Eds.),
Comtemporary  Mathematics, 362, Amer. Math. Soc., Providence , R.I., pp. 53-61 (2004).

90.  R. D. Benguria, and M. C. Depassier,
Variational Calculation of the Period of Nonlinear Oscillators
,
Journal of Statistical Physics, 116,  923-931 (2004). 

89. R. D. Benguria, R. Brummelhuis, P. Duclos, and S. Pérez-Oyarzún,
H2+ in a strong magnetic field described via an exact solvable model
,
Journal of Physics B: Atomic, Molecular and Optical Physics 37, 2311-2320 (2004).

88. R.D. Benguria, M.C. Depassier, and V. Mendez, 
Propagation of fronts of a reaction-convection-diffusion equation

Physical Review E  69,  031106 (7) (2004).

87. R.D. Benguria,
The Lane-Emden equation revisited,
Contemporary Mathematics 327, 11-19 (2003).

86. R.D. Benguria, M.C. Depassier,
Linear and marginal stability for fronts of hyperbolic reaction-diffusion equations
,
Physical Review E  66, 26607(6) (2002).

85. R.D. Benguria and S. Pérez-Oyarzún,
The ultrarelativistic Thomas-Fermi model
,
Journal of Physics A: Mathematical and General 35, 3409-3414 (2002).

84. C.Bandle, R.D. Benguria,
The Brézis-Nirenberg Problem on S³
,
Journal of Differential Equations, 178 , 264 - 279 (2002). 

83. R.D. Benguria,
Rayleigh-Faber-Krahn Inequality
,
in Encyclopaedia of Mathematics, Supplement III, Managing Editor: M. Hazewinkel,
Kluwer Academic Publishers,  pp. 325-327, (2001).

82. R.D. Benguria,
Neumann Eigenvalue
,
in Encyclopaedia of Mathematics, Supplement III, Managing Editor: M. Hazewinkel,
Kluwer Academic Publishers, pp. 280-281, (2001). 

81. R.D. Benguria,
Dirichlet Eigenvalue,
in Encyclopaedia of Mathematics, Supplement III, Managing Editor: M. Hazewinkel,
Kluwer Academic Publishers,  pp. 130-132, (2001).

80. R.D. Benguria, H. Siedentop, and E. Stockmeyer,
Dissociation of homonuclear relativistic molecular ions
,
Annales Henri Poincaré 2, 27- 40 (2001).

79. M. S. Ashbaugh and R. D. Benguria,
A Sharp Bound for the Ratio of the First Two Dirichlet Eigenvalues of a Domain in a Hemisphere of  Sn
,
Transactions of the American Mathematical Society  353, 1055-1087 (2001).

78. R.D. Benguria and M.C. Depassier,
Bounds for Nonlinear Eigenvalue Problems
,
Electronic Journal of Differential Equations, Conf. 06, 23-27 (2001).

77. R. D. Benguria, J. Dolbeault, and M.J. Esteban,
Classification of the solutions of semilinear elliptic problems in a ball
Journal of Differential Equations 167, 438-466 (2000).

76. R.D. Benguria, H. Castillo, and M. Loewe, 
The Dirac equation with a delta potential

Journal of Physics A: Mathematical and General 33, 5315–5320 (2000).

75. R. D. Benguria and M. Loss,
A simple proof of a theorem of Laptev and Weidl
,
Mathematical Research Letters 7, 195-203  (2000).

74. R. D. Benguria and M. C.Depassier,
A Reversed Poincaré Inequality for Monotone Functions
,
Journal of Inequalities and Applications  5, 91-96 (2000).

73. R.D. Benguria and M.C. Depassier,
Variational principle for the limit cycle of Rayleigh's equation
,
in Differential Equations and Mathematical Physics,  (R. Weikard and G. Weinstein, Eds.), 
Studies in Advanced Mathematics, 16, 21-26 (2000).

72. H. Alarcón, R. D. Benguria, P. Duclos, and H. Hogreve,
On the Stability of Positive Molecular Ions
,
Helvetica Physica Acta  72, 386-407 (1999).

71. R. D. Benguria and M. C.Depassier,
Variational principle for limit cycles of the Rayleigh-van der Pol equation
,
Physical Review E 59, 4889-4893 (1999).

70. R. D. Benguria, M. C. Depassier, and M. Favre,
Problemas Resueltos de Electricidad y Magnetismo
,
Ediciones, Universidad Católica de Chile, Santiago de Chile, 1998. ISBN 956-14-0514-8
(Segunda Edición, Santiago de Chile, 2004, Tercera Edición, Santiago de Chile 2008).

69. R. D. Benguria and M. C. Depassier,
A Variational Method for Nonlinear Eigenvalue Problems
,
in Advances in Differential Equations and Mathematical Physics, (Eric Carlen, Evans Harrell, and Michael Loss, Eds.),
Amer. Math. Soc., Contemporary Mathematics, 217, 1-17 (1998).

68. R. D. Benguria and M. C.Depassier, 
Speed of fronts of generalized reaction-diffusion equations
,
Physical Review E 57, 6493-6496 (1998).

67. R. D. Benguria and M. C. Depassier,
Phase Space Derivation of a Variational Principle for One-dimensional Hamiltonian Systems
,
Physics Letters A 240, 144-146 (1998).

66. R. D. Benguria and J. M. Yáñez,
Variational Principle for the Chemical Potential in the Thomas-Fermi Model
,
Journal of Physics A: Mathematical and General 31, 585-593 (1998).

65. M. S. Ashbaugh and R. D. Benguria,
On the Payne-Pólya-Weinberger conjecture on the n-dimensional sphere,
in General Inequalities 7, (C. Bandle , W. N. Everitt, L. Losonczi, and W. Walter, Eds.),
International Series of Numerical Mathematics, 123, pp. 111-128, Birkhäuser Verlag (Basel) 1997.

64. M. S. Ashbaugh, R. D. Benguria, and R. S. Laugesen,
Inequalities for the first eigenvalues of the clamped plate and buckling problems,
in General Inequalities 7, (C. Bandle , W. N. Everitt, L. Losonczi, and W. Walter, Eds.),
International Series of Numerical Mathematics, 123, pp. 95-110, Birkhäuser Verlag (Basel) 1997.

63. R. D. Benguria and M.C . Depassier,
Problemas Resueltos de Mecánica Clásica
,
Ediciones Universidad Católica de Chile, Santiago de Chile, 1996. ISBN 956-14-0403-6.
(Segunda Edición, publicada por Alfaomega Grupo Editor, México, D.F., 1999. ISBN 970-15-0426-7) .

62. R. D. Benguria and M. C. Depassier,
Monotonic Fronts of the Reaction-Diffusion Equation in One Space Dimension
,
in Instabilities and Nonequilibrium Structures V, (E. Tirapegui and W. Zeller, Eds.),
Kluwer Academic Publishers, Dordrecht, pp. 105-110, 1996.

61. R. D. Benguria and M. C. Depassier,
A variational principle for eigenvalue problems of Hamiltonian systems
,
Physical Review Letters 77, 2847-2850 (1996).

60. R. D. Benguria and M. C. Depassier,
Speed of fronts of the reaction-diffusion equation
,
Physical Review Letters  77, 1171-1173 (1996).

59. M. S. Ashbaugh and R. D. Benguria,
Bounds for Ratios of the First, Second, and Third Membrane Eigenvalues
,
in Nonlinear Problems in Applied Mathematics, in honor of Ivar Stakgold on his 70th birthday,
(T.S. Angell, L. P. Cook, R.E. Kleinman y W.E. Olmstead, Eds.), SIAM, Philadelphia, pp. 30-42, 1996.

58. R. D. Benguria, and M. C. Depassier,
Variational Characterization of the Speed of Propagation of Fronts for the Nonlinear Diffusion Equation
,
Communications in Mathematical Physics, 175, 221- 227 (1996).

57. R. D. Benguria,  J. Cisternas, and M. C. Depassier,
Variational Calculations for Thermal Combustion Waves
,
Physical Review E 52, 4410 – 4413 (1995).

56. R. D. Benguria and M. C. Depassier,
A Variational Principle for the Asymptotic Speed of Fronts of the
Density Dependent Diffusion-Reaction Equation
Physical Review E 52, 3285-3287 (1995). 

55. R. D. Benguria, and M. C. Depassier,
Monotonic Fronts in Phase Space, in Differential Equations and Mathematical Physics,

in Differential Equations and Mathematical Physics,
Proceedings of the International Conference, Univ. Alabama at Birmingham
, March 13-17, 1994, (I. W. Knowles, Ed.), pp. 28-36, International Press (Cambridge, Mass.) 1995.

54. M.S. Ashbaugh, and R.D. Benguria,
On Rayleigh's Conjecture for the Clamped Plate and its Generalization to Three Dimensions
,
in Differential Equations and Mathematical Physics,
Proceedings of the International Conference, Univ. Alabama at Birmingham
, March 13-17, 1994, (I. W. Knowles, Ed.),
pp. 17-27, International Press (Cambridge, Mass.) 1995.

53. H. Alarcón and R. D. Benguria,
A Lower Bound on the Size of Molecules
,
Letters in Mathematical Physics 35, 281-289 (1995).

52. M. S. Ashbaugh and R. D. Benguria,
Sharp Upper Bound to the First Nonzero Neumann Eigenvalue for Bounded Domains in Spaces of Constant Curvature
,
Journal of the London Mathematical Society (2) 52, 402-416 (1995).

51. M. S. Ashbaugh and R. D. Benguria,
On Rayleigh's Conjecture for the Clamped Plate and its Generalization to Three Dimensions
Duke Mathematical Journal 78, 1- 17 (1995).

50. R. D. Benguria, 
Sobre la solución de ecuaciones algebraicas
,
Revista del Profesor de Matemáticas, 1, 74-82 (1994).
"On the Solution of Algebraic Equations", translated from the original Spanish version by Mariah Laugesen,
Urbana, Illinois, 2019.

49. M. S. Ashbaugh and R.D . Benguria, 
¿Se puede escuchar la forma de un tambor?,
Gaceta de la Sociedad Matemática de Chile,  7-20 (1994).

48. R. D. Benguria and M. C. Depassier,
Exact fronts for the nonlinear diffusion equation with quintic nonlinearities
,
Physical Review E 50, 3701--3704 (1994).

47. R. D. Benguria and M. C. Depassier,
On the validity of the linear speed selection mechanism for fronts
of the nonlinear diffusion equation,
Physical Review Letters 73, 2272-2274 (1994).

46. M. S. Ashbaugh and R. D. Benguria,
The Range of Values of l3 / l1 and l2 / l1 for the Fixed  Membrane Problem,
Reviews in Mathematical Physics, 6, 999-1009 (1994).
Reprinted in The State of Matter: a volume dedicated to E. H. Lieb, (M. Aizenman and H. Araki, Eds.),
Advances Series in Mathematical Physics 20, pp. 167-182, World Scientific (Singapore) 1994.

45. M. S. Ashbaugh and R.D. Benguria,
Isoperimetric Inequalities for Eigenvalue Ratios
,
in Partial Differential Equations of Elliptic Type, (A. Alvino, E. Fabes, G. Talenti, Eds.)
Symposia Mathematica XXXV,  pp. 1-36, Cambridge University Press (Cambridge, UK) 1994.

44. R. D. Benguria, S. Lorca, and C. Yarur, 
Nonexistence Results for Solutions of Semilinear Elliptic Equations
,
Duke Mathematical Journal 74, 615-634 (1994).

43. M. S. Ashbaugh and R. D. Benguria, 
Bounds for Ratios of Eigenvalues of the Dirichlet Laplacian
,
Proceedings of the American  Mathematical Society 121, 145-150 (1994).

42. R. D. Benguria and M. C. Depassier,
On the existence of monotonic fronts for a class of physical problems described by the equation  lu'''+ u'=f(u)
,
Journal of Physics A: Mathematical and General 27, 1339-1344 (1994).

41. C. M. Alfaro, R. D. Benguria, and M. C. Depassier,
The Role of Dispersion in the Generalized Kuramoto-Sivashinsky Equation
,
in Instabilities and Nonlinear Structures. IV, (E. Tirapegui and W. Zeller, Eds.),
Mathematics and Its Applications 267, pp. 281- 287, Kluwer Academic Publishers ( Dordrecht) 1993.

40. M. S. Ashbaugh and R. D. Benguria,
Isoperimetric Bounds for Higher Eigenvalue Ratios for the N-dimensional Fixed Membrane Problem
,
Proceedings of The Royal Society of Edinburgh 123A, 977-985 (1993).

39. M. S. Ashbaugh and R.D. Benguria,
More Bounds on Eigenvalue Ratios for Dirichlet Laplacians in N Dimensions,
SIAM Journal of Mathematical Analysis  24, 1622-1651 (1993).

38. M. S. Ashbaugh and R. D. Benguria,
Universal Bounds for the Low Eigenvalues of Neumann Laplacians in N Dimensions
,
SIAM Journal of Mathematical Analysis  24, 557- 570 (1993).

37. M. S. Ashbaugh and R. D. Benguria,
Eigenvalue Ratios for Sturm-Liouville Operators,
Journal of Differential Equations 103, 205- 219 (1993).

36. C. M. Alfaro, R. D. Benguria, and M. C. Depassier,
Finite Mode Analysis of the Kuramoto-Sivashinsky Equation Modified by Dispersion
,
Physica D 61, 1-5 (1992).

35. R. D. Benguria, S. Hoops, and H. Siedentop,
Bounds on the excess charge and the ionization energy for the Hellmann-Weizsäcker model
,
Annales de l’Institut Henri Poincaré (A) Physique Théorique 57, 47- 65 (1992).

34. M. S. Ashbaugh and R. D. Benguria,
A Second Proof of the Payne-Pólya-Weinberger Conjecture,
Communications in Mathematical  Physics 147, 181-190 (1992).

33. R. D. Benguria and M. C. Depassier,
Three mode truncation of a model equation for systems with long wave oscillatory instability
,
Physical Review A 45, 5566-5571 (1992).

32. M. S. Ashbaugh and R. D. Benguria,
A Sharp Bound for the Ratio of the First Two Eigenvalues of Dirichlet Laplacians and Extensions,
Annals of Mathematics 135, 601-628 (1992).

31. M. S. Ashbaugh and R. D. Benguria,
Isoperimetric Bound for l3/l
2  for the Membrane Problem,
Duke Mathematical Journal 63, 333-341 (1991)

30.  M. S. Ashbaugh and R. D. Benguria,
Proof of the Payne-Pólya-Weinberger Conjecture
,
Bulletin of the American Mathematical Society  25, 19-29 (1991).

29. M. S. Ashbaugh, R. D. Benguria, and C. Yarur,
Properties of the positive solution of a generalized Thomas-Fermi-von Weizsäcker equation
,
Duke Mathematical Journal 63, 199-215 (1991).   

28. R. D. Benguria and C. Yarur,
Sharp condition on the decay of the potential for the absence of a zero energy ground state of the Schrödinger equation,

Journal of Physics A: Mathematical and  General 23, 1513-1518 (1990).

27. M. S. Ashbaugh and R. D. Benguria,
Some Eigenvalue Inequalities for a Class of Jacobi Matrices
,
Linear Algebra and its Applications 136, 215-234 (1990);
Addendum, Linear Algebra and its Applications 149, 277 (1991).

26. R.D. Benguria and C.Yarur,
Symmetry Properties of the solutions to Thomas-Fermi-von Weizsäcker type equations
,
Transactions of the American Mathematical Society 320, 665-675 (1990).
 
25. R. D. Benguria and M. C. Depassier,
Oscillatory Instabilities in BénardMarangoni Convection in a Fluid Bounded Above by a Free Surface,
in Instabilities and Nonlinear Structures II: Dynamical Systems and Instabilities, (E. Tirapegui and D. Villaroel, Eds.),
Mathematics and Its Applications 50, pp. 221-225, Kluwer Ac. Pub. (Dordrecht) 1989.

24. R. D. Benguria and M. C. Depassier,
Equations of the Korteweg-de Vries type with nontrivial conserved quantities,
Journal of Physics A: Mathematical and General 22, 4135-4142 (1989).

23. M. S. Ashbaugh and R. D. Benguria,
Optimal Bounds for Ratios of Eigenvalues of One-Dimensional Schrödinger Operators with Dirichlet Boundary Conditions and Positive Potentials
,
Communications in Mathematical Physics 124, 403-415 (1989).

22. R. D. Benguria and M. C. Depassier,
On the linear stability theory of Bénard-Marangoni convection,
Physics of Fluids A 1, 1123-1127 (1989).

21. M. S. Ashbaugh and R.D. Benguria,
Optimal Lower Bound for the Gap Between the First Two Eigenvalues of One-Dimensional Schrödinger operators with Symmetric Single-Well Potentials
,
Proceedings of the American Mathematical Society 105, 419-424 (1989).

20. M. S. Ashbaugh and R. D. Benguria,
Optimal Lower Bounds for Eigenvalue Gaps for Schrödinger Operators with Symmetric Single-Well Potentials and Related Results, in Maximum Principles and Eigenvalue Problems in Partial Differential Equations, (P. Schaefer, Ed.),
Pitman Research Notes in Mathematical Series 175,  pp. 134-145, Longman Sci. Tech. (Harlow) 1988.

19. M. S. Ashbaugh and R. D. Benguria,
Log-Concavity of the Ground State of Schrödinger Operators: A New Proof of the Baumgartner, Grosse, Martin Inequality,
Physics  Letters A 131, 273-276 (1988).

18. M. S. Ashbaugh and R. D. Benguria,
On the Ratio of the First Two Eigenvalues of Schrödinger Operators with Positive Potentials
,
in Differential Equations and Mathematical Physics,
Proceedings of an International Conference held in Birmingham, Alabama, USA, March 3-8, 1986,
Lecture Notes in Mathematics, 1285 (I.W. Knowles Y. Saito, Eds.)  pp. 16-25, Springer-Verlag (Berlin) 1987.

17. R. D. Benguria and M. C. Depassier,
Oscillatory Instabilities in the Rayleigh-Bénard Problem with a Free Surface
,
Physics of Fluids 30, 1678-1682 (1987).

16. M. S. Ashbaugh and R .D. Benguria,
Best Constant for the Ratio of the First Two Eigenvalues of One-Dimensional Schrödinger Operators with Positive Potentials
,
Proceedings of the American Mathematical Society  99, 598-599 (1987).

15. R. D. Benguria and L. Jeanneret,
Existence and Uniqueness of Positive Solutions of Semilinear Elliptic Equations with Coulomb Potentials on R3,
Communications in Mathematical   Physics 104, 291-306 (1986).

14. R. D. Benguria,
A Note on the Gap Between the first two Eigenvalues for the Schrödinger Operator
,
Journal of  Physics A: Mathematical & General 19, 477-478 (1986).

13. R. D. Benguria and E. H. Lieb,
The Most Negative Ion in the Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules
,
Journal of Physics B: Atomic and Molecular Physics 18, 1041-1059 (1985).

12.  R. D. Benguria and E. H. Lieb,
Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle
,
Physical Review Letters  50, 1771-1774 (1983).

11. R. Benguria and M. C. Depassier,
Upper and Lower Bounds for Eigenvalues of Nonlinear Elliptic Equations. I. The Lowest Eigenvalue
,
Journal of Mathematical Physics 24, 501-503 (1983).

10. R. Benguria,
Dependence of the Thomas-Fermi Energy on the Nuclear Coordinates
,
Communications in Mathematical Physics  81, 419-428 (1981).

9. R. Benguria, H. Brezis, and E. H. Lieb,
The Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules
,
Communications in Mathematical  Physics 79, 167-180 (1981).

8. R. Benguria and M. Kac,
Quantum Langevin Equation
,
Physical  Review Letters  46, 1-4 (1981).

7. D. Levi and R. Benguria,
Backlund Transformations and Nonlinear Differential-Difference Equations,
Proceedings of the National Academy of Sciences ( USA) 77, 5025-5027 (1980).

6. R. Benguria and K. M. Case,
Backlund Transformations for Multi-dimensional Sine-Gordon Equations
,
Proceedings of the National Academy of Sciences ( USA) 77, 4393-4394 (1980).

5. R. Benguria and E. H. Lieb,
The Positivity of the Pressure in Thomas-Fermi Theory
,
Communications in  Mathematical Physics  63, 193-218 (1978);
Erratum
, Communications in Mathematical Physics 63, 193-218 (1978).

4.  R. Benguria and E. H. Lieb, 
Many-Body Atomic Potentials in Thomas-Fermi Theory

Annals of Physics 110, 34-45 (1978).

3. R. Benguria, P. Cordero, and C. Teitelboim,
Aspects of Hamiltonian Dynamics of Interacting Gravitational Gauge and Higgs Fields with Applications to Spherical Symmetry

Nuclear Physics B 122, 61-99 (1977).

2. R. Benguria,
Electrodynamics and the Equations of Motion of Charged Particles with Spin
,
Physical Review D 13, 274-278 (1976).

1. P. Arroyo, R. Benguria , E. Collados, and J. Tohá,
Low Self-Complementarity of Cytochrom-C Messenger RNA, a Structural and Functional Restriction at the Molecular Level
,
Journal of Theoretical Biology 54, 153-166 (1975). 



Remark: The articles numbers [4], [5], [9], [12] and [13] of the above list have been reprinted in: The Stability of Matter: From Atoms to Stars, Selecta of Elliott H. Lieb, Edited by W. Thirring, Springer-Verlag (NY) (1991).


Last revised (October 28, 2019).