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Applications of Morse theory to some nonlinear elliptic equations with resonance at zero. (English) Zbl 1304.35309
Summary: In this paper we study the existence and multiplicity of solutions for some nonlinear elliptic boundary value problems with resonance at zero by applying Morse theory. We do not impose additional global condition on the nonlinearities, except for a subcritical growth condition.
MSC:
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35B34 Resonance in context of PDEs
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