Relative Morse index and multiple brake orbits of asymptotically linear Hamiltonian systems in the presence of symmetries |
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Authors: | Duanzhi Zhang |
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Institution: | a School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China b School of Mathematical Sciences, Peking University, Beijing 100871, PR China |
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Abstract: | In this paper, we define a relative Morse index for two continuous symmetric matrices paths in R2n satisfying condition (B1) and study its relation with the Maslov-type indices under brake orbit boundary value of these two symmetric matrices paths. As applications, using this relation we obtain a multiple existence of periodic brake orbit solutions of asymptotically linear Hamiltonian system in the presence of symmetries. |
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Keywords: | 58E05 70H05 34C25 |
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