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

MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35J60 Nonlinear elliptic equations
47J05 Equations involving nonlinear operators (general)
35J20 Variational methods for second-order elliptic equations
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[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.\bf19, 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, (), 161-177
[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., (), 141-195
[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) · Zbl 0436.58006
[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, () · Zbl 0632.34036
[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, I-C, 347-356, (1982) · Zbl 0511.58017
[26] De Candia, A.M., Teoria dei punti critici in presenza di simmetrie ed applicazioni, ()
[27] Krasnoselski, M.A., Topological methods in the theory of nonlinear integral equations, (1964), MacMillan New York
[28] Rabinowitz, P.H., Free vibrations for a semilinear wave equations, Communs. pure appl. math., 31, 31-68, (1978) · Zbl 0341.35051
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