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Abstract critical point theorems and applications to some nonlinear problems with ”strong” resonance at infinity. (English) Zbl 0522.58012

58E05Abstract critical point theory
35J60Nonlinear elliptic equations
47J05Equations involving nonlinear operators (general)
35J20Second order elliptic equations, variational methods
Full Text: DOI
[1] Amann, H.: Saddle points and multiple solutions of differential equations. Math. Z. 169, 127-166 (1979) · Zbl 0414.47042
[2] Amann, H.; Zehnder, E.: Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Annali scu. Norm. sup. Pisa 7, 539-603 (1980) · Zbl 0452.47077
[3] Hess P., Solutions nontriviales d’un problème aux limites elliptique nonlineaire, C.r. hebd. Séanc. Acad. Sci. Paris.
[4] Castro, A.; Lazer, A.: Critical points theory and the number of solutions of a nonlinear Dirichlet problem. Annali mat. Pura appl. 120, 113-137 (1979) · Zbl 0426.35038
[5] Landesman E.A. & Lazer A.C., Nonlinear perturbations of linear elliptic boundary values problems at resonance, J. math. Mech. 19, 609-623. · Zbl 0193.39203
[6] Brezis, H.; Nirenberg, L.: Characterizations of the ranges of some nonlinear operators and applications to the boundary value problems. Annali scu. Norm. sup. Pisa 5, 225-326 (1978) · Zbl 0386.47035
[7] Ahmad, S.; Lazer, A. C.; Paul, J. L.: Elementary critical point theory and perturbations of elliptic boundary value at resonance. Indiana univ. Math. J. 25, 933-944 (1976) · Zbl 0351.35036
[8] Rabinowitz, P. H.: Some mini-MAX theorems and applications to nonlinear partial differential equations. Nonlinear analysis, 161-177 (1978)
[9] Ambrosetti, A.; Mancini, G.: Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part. Annali scu. Norm. sup. Pisa 5, 15-38 (1978) · Zbl 0375.35024
[10] Ambrosetti, A.; Mancini, G.: Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of simple eigenvalue. J. diff. Eqns 28, 220-245 (1978) · Zbl 0393.35032
[11] Hess, P.: Nonlinear perturbations of linear elliptic and parabolic problems at resonance: existence of multiple solutions. Annali scu. Norm. sup. Pisa 5, 527-537 (1978) · Zbl 0392.35051
[12] Rabinowitz, P. H.: G.prodi variantional methods for nonlinear eigenvalue problems. Variantional methods for nonlinear eigenvalue problems, 141-195 (1974)
[13] Thews, K.: Non-trivial solutions of elliptic equations at resonance. Proc. R. Soc. edinb. 85A, 119-129 (1980) · Zbl 0431.35040
[14] Clark, D. C.: A variant of Ljusternik-schnirelman theory. Indiana univ. Math. J. 22, 65-74 (1972) · Zbl 0228.58006
[15] Cerami, G.: Un criterio di esistenza per i punti critici su varietà illimitate. Rc. ist. Lomb. sci. Lett. 112, 332-336 (1978)
[16] Benci, V.: On the critical point theory for indefinite functional in the presence of symmetries. Trans. am. Math. soc. 274, 533-572 (1982) · Zbl 0504.58014
[17] Benci, V.; Capozzi, A.; Fortunato, D.: Periodic solutions of Hamiltonian systems with a prescribed period. Math. res. Center, tech. Summary report no. 2508 (1983) · Zbl 0525.70021
[18] Cerami G., Sull’esistenza di autovalori per un problema al contorno non lineare, Annali Mat. pura appl., to appear. · Zbl 0441.35054
[19] Palais, R. S.: Ljusternik-schnirelman theory on Banach manifolds. Topology 5, 115-132 (1966) · Zbl 0143.35203
[20] Benci, V.; Rabinowitz, P. H.: Critical point theorems for indefinite functionals. Invent. math. 52, 241-273 (1979) · Zbl 0465.49006
[21] Ambrosetti, A.; Rabinowitz, P. H.: Dual variational methods in critical points theory and applications. J. funct. Analysis 14, 349-381 (1973) · Zbl 0273.49063
[22] Benci, V.: Some critical point theorems and applications. Communs. pure appl. Math. 33 (1980) · Zbl 0472.58009
[23] Rabinowitz, P. H.: Some critical point theorems and applications to semilinear elliptic partial differential equations. Annali scu. Norm. sup. Pisa 2, 215-223 (1978) · Zbl 0375.35026
[24] Faddell, E. R.; Rabinowitz, P. H.: Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems. Inv. math. 45, 139-174 (1978) · Zbl 0403.57001
[25] Bartolo, P.: An extension of the krasnoselskj genus. B.i.m.i. 1, No. I-C, 347-356 (1982) · Zbl 0511.58017
[26] De Candia, A. M.: Teoria dei punti critici in presenza di simmetrie ed applicazioni. Thesis (1982)
[27] Krasnoselski, M. A.: Topological methods in the theory of nonlinear integral equations. (1964)
[28] Rabinowitz, P. H.: Free vibrations for a semilinear wave equations. Communs. pure appl. Math. 31, 31-68 (1978) · Zbl 0341.35051