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1. | Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania, Department of Mathematics, University of Craiova, 200585 Craiova, Romania |
References:
[1] |
A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications,, J. Functional Analysis, 14 (1973), 349.
doi: 10.1016/0022-1236(73)90051-7. |
[2] |
G. Bonanno and S. A. Marano, Positive solutions of elliptic equations with discontinuous nonlinearities,, Topol. Methods Nonlinear Anal., 8 (1996), 263.
|
[3] |
H. Brezis, "Analyse Fonctionnelle. Théorie et Applications,", Collection Mathématiques Appliqueées pour la Maîtrise, (1983).
|
[4] |
H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles,, Bull. Amer. Math. Soc., 8 (1983), 409.
doi: 10.1090/S0273-0979-1983-15105-4. |
[5] |
H. Brezis and L. Nirenberg, Remarks on finding critical points,, Comm. Pure Appl. Math., 44 (1991), 939.
doi: 10.1002/cpa.3160440808. |
[6] |
S. Carl and D. Motreanu, Constant-sign and sign-changing solutions for nonlinear eigenvalue problems,, Nonlinear Anal., 68 (2008), 2668.
doi: 10.1016/j.na.2007.02.013. |
[7] |
F. Clarke, A classical variational principle for periodic Hamiltonian trajectories,, Proc. Amer. Math. Soc., 76 (1979), 186.
|
[8] |
F. Clarke, Periodic solutions to Hamiltonian inclusions,, J. Differential Equations, 40 (1981), 1.
doi: 10.1016/0022-0396(81)90007-3. |
[9] |
I. Ekeland, A perturbation theory near convex Hamiltonian systems,, J. Differential Equations, 50 (1983), 407.
doi: 10.1016/0022-0396(83)90069-4. |
[10] |
R. Filippucci, P. Pucci and F. Robert, On a $p$-Laplace equation with multiple critical nonlinearities,, J. Math. Pures Appl., 91 (2009), 156.
doi: 10.1016/j.matpur.2008.09.008. |
[11] |
N. Ghoussoub and D. Preiss, A general mountain pass principle for locating and classifying critical points,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (1989), 321.
|
[12] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order,", Reprint of the 1998 edition, (1998).
|
[13] |
A. Kristály, V. Rădulescu and Cs. Varga, "Variational Principles in Mathematical Physics, Geometry, and Economics. Qualitative Analysis of Nonlinear Equations and Unilateral Problems,", Encyclopedia of Mathematics and its Applications, 136 (2010).
|
[14] |
E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance,, J. Math. Mech., 19 (): 609.
|
[15] |
S. A. Marano and D. Motreanu, Existence of two nontrivial solutions for a class of elliptic eigenvalue problems,, Arch. Math. (Basel), 75 (2000), 53.
|
[16] |
R. Palais, Lusternik-Schnirelmann theory on Banach manifolds,, Topology, 5 (1966), 115.
doi: 10.1016/0040-9383(66)90013-9. |
[17] |
R. Palais and S. Smale, A generalized Morse theory,, Bull. Amer. Math. Soc., 70 (1964), 165.
doi: 10.1090/S0002-9904-1964-11062-4. |
[18] |
P. Pucci and V. Rădulescu, The impact of the mountain pass theory in nonlinear analysis: A mathematical survey,, Boll. Unione Mat. Ital., IX (2010), 543. Google Scholar |
[19] |
P. Pucci and J. Serrin, Extensions of the mountain pass theorem,, J. Funct. Anal., 59 (1984), 185.
doi: 10.1016/0022-1236(84)90072-7. |
[20] |
P. Pucci and J. Serrin, A mountain pass theorem,, J. Differential Equations, 60 (1985), 142.
doi: 10.1016/0022-0396(85)90125-1. |
[21] |
P. Pucci and J. Serrin, The structure of the critical set in the mountain pass theorem,, Trans. Amer. Math. Soc., 299 (1987), 115.
doi: 10.1090/S0002-9947-1987-0869402-1. |
[22] |
V. Rădulescu, "Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations: Monotonicity, Analytic, and Variational Methods,", Contemporary Mathematics and Its Applications, 6 (2008).
|
[23] |
V. Rădulescu, Remarks on a limiting case in the treatment of nonlinear problems with mountain pass geometry,, Universitatis Babes-Bolyai Mathematica, LV (2010), 99. Google Scholar |
[24] |
J. Toland, A duality principle for nonconvex optimisation and the calculus of variations,, Arch. Rational Mech. Anal., 71 (1979), 41.
doi: 10.1007/BF00250669. |
[25] |
X. M. Zheng, Un résultat de non-existence de solution positive pour une équation elliptique,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), 91.
|
show all references
References:
[1] |
A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications,, J. Functional Analysis, 14 (1973), 349.
doi: 10.1016/0022-1236(73)90051-7. |
[2] |
G. Bonanno and S. A. Marano, Positive solutions of elliptic equations with discontinuous nonlinearities,, Topol. Methods Nonlinear Anal., 8 (1996), 263.
|
[3] |
H. Brezis, "Analyse Fonctionnelle. Théorie et Applications,", Collection Mathématiques Appliqueées pour la Maîtrise, (1983).
|
[4] |
H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles,, Bull. Amer. Math. Soc., 8 (1983), 409.
doi: 10.1090/S0273-0979-1983-15105-4. |
[5] |
H. Brezis and L. Nirenberg, Remarks on finding critical points,, Comm. Pure Appl. Math., 44 (1991), 939.
doi: 10.1002/cpa.3160440808. |
[6] |
S. Carl and D. Motreanu, Constant-sign and sign-changing solutions for nonlinear eigenvalue problems,, Nonlinear Anal., 68 (2008), 2668.
doi: 10.1016/j.na.2007.02.013. |
[7] |
F. Clarke, A classical variational principle for periodic Hamiltonian trajectories,, Proc. Amer. Math. Soc., 76 (1979), 186.
|
[8] |
F. Clarke, Periodic solutions to Hamiltonian inclusions,, J. Differential Equations, 40 (1981), 1.
doi: 10.1016/0022-0396(81)90007-3. |
[9] |
I. Ekeland, A perturbation theory near convex Hamiltonian systems,, J. Differential Equations, 50 (1983), 407.
doi: 10.1016/0022-0396(83)90069-4. |
[10] |
R. Filippucci, P. Pucci and F. Robert, On a $p$-Laplace equation with multiple critical nonlinearities,, J. Math. Pures Appl., 91 (2009), 156.
doi: 10.1016/j.matpur.2008.09.008. |
[11] |
N. Ghoussoub and D. Preiss, A general mountain pass principle for locating and classifying critical points,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (1989), 321.
|
[12] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order,", Reprint of the 1998 edition, (1998).
|
[13] |
A. Kristály, V. Rădulescu and Cs. Varga, "Variational Principles in Mathematical Physics, Geometry, and Economics. Qualitative Analysis of Nonlinear Equations and Unilateral Problems,", Encyclopedia of Mathematics and its Applications, 136 (2010).
|
[14] |
E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance,, J. Math. Mech., 19 (): 609.
|
[15] |
S. A. Marano and D. Motreanu, Existence of two nontrivial solutions for a class of elliptic eigenvalue problems,, Arch. Math. (Basel), 75 (2000), 53.
|
[16] |
R. Palais, Lusternik-Schnirelmann theory on Banach manifolds,, Topology, 5 (1966), 115.
doi: 10.1016/0040-9383(66)90013-9. |
[17] |
R. Palais and S. Smale, A generalized Morse theory,, Bull. Amer. Math. Soc., 70 (1964), 165.
doi: 10.1090/S0002-9904-1964-11062-4. |
[18] |
P. Pucci and V. Rădulescu, The impact of the mountain pass theory in nonlinear analysis: A mathematical survey,, Boll. Unione Mat. Ital., IX (2010), 543. Google Scholar |
[19] |
P. Pucci and J. Serrin, Extensions of the mountain pass theorem,, J. Funct. Anal., 59 (1984), 185.
doi: 10.1016/0022-1236(84)90072-7. |
[20] |
P. Pucci and J. Serrin, A mountain pass theorem,, J. Differential Equations, 60 (1985), 142.
doi: 10.1016/0022-0396(85)90125-1. |
[21] |
P. Pucci and J. Serrin, The structure of the critical set in the mountain pass theorem,, Trans. Amer. Math. Soc., 299 (1987), 115.
doi: 10.1090/S0002-9947-1987-0869402-1. |
[22] |
V. Rădulescu, "Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations: Monotonicity, Analytic, and Variational Methods,", Contemporary Mathematics and Its Applications, 6 (2008).
|
[23] |
V. Rădulescu, Remarks on a limiting case in the treatment of nonlinear problems with mountain pass geometry,, Universitatis Babes-Bolyai Mathematica, LV (2010), 99. Google Scholar |
[24] |
J. Toland, A duality principle for nonconvex optimisation and the calculus of variations,, Arch. Rational Mech. Anal., 71 (1979), 41.
doi: 10.1007/BF00250669. |
[25] |
X. M. Zheng, Un résultat de non-existence de solution positive pour une équation elliptique,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), 91.
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