Existence of homoclinic solution for the second order Hamiltonian systems
Existence of homoclinic solution for the second order Hamiltonian systems
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DOI：
10.1016/j.jmaa.2003.10.026
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发表时间：
2004-03
影响因子：
1.3
通讯作者：
Z. Ou;Chunlei Tang
中科院分区：
文献类型：
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作者：
Z. Ou;Chunlei Tang
利用临界点理论中的极小极大方法，特别是推广的山路定理，得到了一类非自治二阶Hamilton系统u ∈（t）-L（t）u（t）+<$W（t，u（t））=0，<$t∈R的同宿解的存在性定理，其中L（t）对所有t∈R不必一致正定，W（t，x）满足超二次条件W（t，x）/|X| 2→+∞ as| X| →∞在t中一致，并且不需要满足全局Ambrosetti-Rabinowitz条件。
An existence theorem of homoclinic solution is obtained for a class of the nonautonomous second order Hamiltonian systems u ̈ (t)−L(t)u(t)+∇W(t,u(t))=0 , ∀t∈R, by the minimax methods in the critical point theory, specially, the generalized mountain pass theorem, where L(t) is unnecessary uniformly positively definite for all t∈R, and W(t,x) satisfies the superquadratic condition W(t,x)/|x|2→+∞ as |x|→∞ uniformly in t, and need not satisfy the global Ambrosetti–Rabinowitz condition.