Electron. J. Differential Equations, Vol. 2017 (2017), No. 205, pp. 1-7.

Homoclinic solutions for a class of second-order Hamiltonian systems with locally defined potentials

Xiang Lv

Abstract:
In this article, we establish sufficient conditions for the existence of homoclinic solutions for a class of second-order Hamiltonian systems
$$ \ddot u(t)-L(t)u(t)+\nabla W\bigl(t,u(t)\bigr)=f(t), $$
where L(t) is a positive definite symmetric matrix for all $t\in\mathbb{R}$. It is worth pointing out that the potential function W(t,u) is locally defined and can be superquadratic or subquadratic with respect to u.

Submitted March 13, 2017. Published September 7, 2017.
Math Subject Classifications: 34C37, 70H05, 58E05.
Key Words: Homoclinic solutions; Hamiltonian systems; variational methods.

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Xiang Lv
Department of Mathematics
Shanghai Normal University
Shanghai 200234, China
email: lvxiang@shnu.edu.cn

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