Nontrivial homoclinic orbits for second-order singular and periodic Hamiltonian systems |
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| Authors: | Chengyue Li Tianyou Fan Mingsheng Tong |
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| Institution: | (1) Research Center of Materials Science, Beijing Institute of Technology, 100081 Beijing, China;(2) Department of Mathematics, Central University for Nationalities, 100081 Beijing, China;(3) Computer Center, Beijing Institute of Technology, 100081 Beijing, China |
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| Abstract: | The existence of nontrivial homoclinic orbits of periodic Hamiltonian systems:q + V′q(t, q) = 0 is proved, whereq = (q
1,q
2,...,q
n),n> 2;V(t, q): ℝ1 × ℝn |e| → ℝ1 is a potential with a singularity, i.e. -V(t, q)→+∞, asq→e. The main assumptions are Gordon-strong force condion and the uniqueness of a global maximum ofV(t, q). |
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| Keywords: | Hamiltonian systems strong force condition homoclinic orbit |
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