Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems
Annales de l'I.H.P. Analyse non linéaire, Volume 3 (1986) no. 2, pp. 77-109.
@article{AIHPC_1986__3_2_77_0,
author = {Szulkin, Andrzej},
title = {Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {77--109},
publisher = {Gauthier-Villars},
volume = {3},
number = {2},
year = {1986},
zbl = {0612.58011},
mrnumber = {837231},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1986__3_2_77_0/}
}
TY  - JOUR
AU  - Szulkin, Andrzej
TI  - Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1986
DA  - 1986///
SP  - 77
EP  - 109
VL  - 3
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1986__3_2_77_0/
UR  - https://zbmath.org/?q=an%3A0612.58011
UR  - https://www.ams.org/mathscinet-getitem?mr=837231
LA  - en
ID  - AIHPC_1986__3_2_77_0
ER  - 
%0 Journal Article
%A Szulkin, Andrzej
%T Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems
%J Annales de l'I.H.P. Analyse non linéaire
%D 1986
%P 77-109
%V 3
%N 2
%I Gauthier-Villars
%G en
%F AIHPC_1986__3_2_77_0
Szulkin, Andrzej. Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems. Annales de l'I.H.P. Analyse non linéaire, Volume 3 (1986) no. 2, pp. 77-109. http://archive.numdam.org/item/AIHPC_1986__3_2_77_0/

[1] A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications. J. Func. Anal., t. 14, 1973, p. 349-381. | MR | Zbl

[2] J.P. Aubin and I. Ekeland, Applied Nonlinear Anahlsis. Wiley, New York, 1984. | MR | Zbl

[3] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces. Editura Academiei. Bucarest and Nordhoff, Leyden, 1976. | MR | Zbl

[4] H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. North-Holland, Amsterdam, 1973. | MR | Zbl

[5] H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. In: Contributions to Nonlinear Functional Analysis. E. Zarantanello ed., Academic Press, New York, 1971, p. 101-156. | MR | Zbl

[6] H. Brézis, Some variational problems with lack of compactness, Proc. of the 1983 AMS Summer Institute on Nonl. Func. Anal. and Appl., Amer. Math. Soc. (to appear). | MR | Zbl

[7] H. Brézis and L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Ann. Scuola Norm. Sup. Pisa, Ser. IV, t. 5, 1978, p. 225-326. | Numdam | MR | Zbl

[8] K.C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl., t. 80, 1981, p. 102-129. | MR | Zbl

[9] D.C. Clark, A variant of the Ljusternik-Schnirelmann theory. Indiana Univ. Math. J., t. 22, 1972, p. 65-74. | MR | Zbl

[10] J.P. Dias, Variational inequalities and eigenvalue problems for nonlinear maximal monotone operators in a Hilbert space. Amer. J. Math., t. 97, 1975, p. 905-914. | MR | Zbl

[11] J.P. Dias and J. Hernández, A Sturm-Liouville theorem for some odd multivalued maps. Proc. Amer. Math. Soc., t. 53, 1975, p. 72-74. | MR | Zbl

[12] G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics. Springer, Berlin, 1976. | MR | Zbl

[13] I. Ekeland, Nonconvex minimization problems. Bull. Amer. Math. Soc., t. 1, 1979, p. 443-474. | MR | Zbl

[14] D. G. De Figueiredo and S. Solimini, A variational approach to superlinear elliptic problems. Comm. P. D. E., t. 9, 1984, p. 699-717. | MR | Zbl

[15] L.I. Hedberg, Spectral synthesis and stability in Sobolev spaces. Springer Lecture Notes in Mathematics, t. 779, 1980, p. 73-103. | MR | Zbl

[16] S.T. Hu, Homotopy Theory, Academic Press, New York, 1959. | MR | Zbl

[17] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. Academic Press, New York, 1980. | MR | Zbl

[18] K. Kuratowski, Topologie I, PWN, Warsaw, 1958. | Zbl

[19] J. Mawhin and M. Willem, Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations. J. Diff. Eq., t. 52, 1984, p. 264- 287. | MR | Zbl

[20] L. Nirenberg, Variational and topological methods in nonlinear problems. Bull. Amer. Math. Soc., t. 4, 1981, p. 267-302. | MR | Zbl

[21] P.H. Rabinowitz, Variational methods for nonlinear eigenvalue problems, Proc. Sym. on Eigenvalues of Nonlinear Problems. Edizioni Cremonese, Rome, 1974, p. 143-195. | MR

[22] P.H. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations. In: Nonlinear Analysis, A collection of papers in honor of E. Rothe, L. Cesari, R. Kannan and H. F. Weinberger ed., Academic Press, New York, 1978, p. 161-177. | MR | Zbl

[23] P.H. Rabinowitz, Some critical point theorems and applications to semilinear elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. IV, t. 5, 1978, p. 215-223. | Numdam | MR | Zbl

[24] P.H. Rabinowitz, Some aspects of critical point theory, MRC Tech. Rep. # 2465, Madison, Wisconsin, 1983.

[25] J.T. Schwartz, Nonlinear Functional Analysis. Gordon and Breach, New York, 1969. | MR | Zbl

[26] M. Struwe, Multiple solutions of differential equations without the Palais-Smale condition. Math. Ann., t. 261, 1982, p. 399-412. | MR | Zbl

[27] M. Struwe, Generalized Palais-Smale conditions and applications. Vorlesungsreihe SFB # 17, Bonn, 1983. | Zbl

[28] I. Ekeland and J.M. Lasry, On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math., t. 112, 1980, p. 283-319. | MR | Zbl