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Zbl 1173.34330
Zhang, Ziheng; Yuan, Rong
Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 71, No. 9, A, 4125-4130 (2009). ISSN 0362-546X

Summary: We consider the existence of homoclinic solutions for the following second-order non-autonomous Hamiltonian system: $$\ddot q-L(t)q+W_q(t,q)=0,\tag HS$$ where $L(t)\in C(\Bbb R,\Bbb R^{n^2})$ is a symmetric and positive definite matrix for all $t\in\Bbb R$, $W(t,q)=a(t)|q|^\gamma$ with $a(t):\Bbb R\to\Bbb R^+$ source is a positive continuous function and $1<\gamma<2$ is a constant. Adopting some other reasonable assumptions for $L$ and $W$, we obtain a new criterion for guaranteeing that (HS) has one nontrivial homoclinic solution by use of a standard minimizing argument in critical point theory. Recent results from the literature are generalized and significantly improved.

MSC 2000:: *34C37 Homoclinic and heteroclinic solutions of ODE
37J45 Periodic, homoclinic and heteroclinic orbits, etc.
47J30 Variational methods

Keywords: homoclinic solutions; critical point; variational methods

Cited in: Zbl 1237.37044 Zbl 1230.37079

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