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Computations of critical groups and applications to some differential equations at resonance. (English) Zbl 1123.58007

The author computes the critical groups of a functional with generalized Ahmad-Lazer-Paul type conditions both at zero and infinity, and applies the abstract results to the study of existence of nontrivial solutions to second order Hamiltonian systems and elliptic boundary value problems, which may be resonant both at zero and infinity.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
34B15 Nonlinear boundary value problems for ordinary differential equations
35J65 Nonlinear boundary value problems for linear elliptic equations
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