Computations of critical groups and applications to asymptotically linear wave equation and beam equation |
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| Authors: | Pingan Zeng Jiaquan Liu Yuxia Guo |
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| Institution: | a School of Mathematics, Peking University, Beijing, 100871, PR China
b Department of Mathematics, Tsinghua University, Beijing, 100084, PR China |
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| Abstract: | In this paper, by using the Morse index theory for strongly indefinite functionals developed in Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero. |
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| Keywords: | Morse index theory Critical groups Wave equation Beam equation |
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