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A resonance case for an asymptotically linear vibrating string equation. (English) Zbl 0465.35006


MSC:

35B10 Periodic solutions to PDEs
35L70 Second-order nonlinear hyperbolic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35A15 Variational methods applied to PDEs
35P05 General topics in linear spectral theory for PDEs
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References:

[1] H. Amann and E. Zehnder, ”Multiple Periodic Solutions for a Class of Nonlinear Autonomous Wave Equations,” preprint. · Zbl 0481.35061
[2] Ambrosetti, A.; Rabinowitz, P. H.: Dual variational methods in critical point theory and applications. J. funct. Anal. 14, 349-381 (1973) · Zbl 0273.49063
[3] V. Benci, A geometrical index for the group S1 and some applications to the research of periodic solutions of O.D.E.s, to appear.
[4] Brezis, H.; Coron, J. M.; Nirenberg, L.: Free vibrations for a nonlinear wave equation and a theorem of P. H. rabinowitz. Comm. pure appl. Math. 33, 667-689 (1980) · Zbl 0484.35057
[5] K. C. Chang, S. P. Wu, and S. J. Li, ”Multiple Periodic Solutions for an Asymptotically Linear Wave Equation,” preprint. · Zbl 0465.35007
[6] Clark, D. C.: A variant of Ljusternik-Schnirelmann theory. Indiana univ. J. 22, 65-74 (1972) · Zbl 0228.58006
[7] Fadell, E. R.; Rabinowitz, P. H.: Generalized cohomologial index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems. Invent. math. 45, 139-174 (1978) · Zbl 0403.57001
[8] Rabinowitz, P. H.: G.prodi variational methods for nonlinear eigenvalue problems. Variational methods for nonlinear eigenvalue problems, 141-195 (1974) · Zbl 0278.35040
[9] Rabinowitz, P. H.: Some minimax theorems and applications to nonlinear partial differential equations. Nonlinear analysis, 161-177 (1978) · Zbl 0466.58015
[10] Rabinowitz, P. H.: A variational method for finding periodic solutions of differential equations. Nonlinear evolution equations, 225-251 (1978)
[11] Thews, K.: Multiple solutions for elliptic boundary value problems with odd nonlinearities. Math. Z. 163, 163-175 (1978) · Zbl 0372.35035
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