Electron. J. Diff. Equ., Vol. 2016 (2016), No. 66, pp. 1-12.

Multiple homoclinic solutions for superquadratic Hamiltonian systems

Wei Jiang, Qingye Zhang

Abstract:
In this article we study the existence of infinitely many homoclinic solutions for a class of second-order Hamiltonian systems
$$ \ddot{u}-L(t)u+W_u(t,u)=0, \quad \forall t\in\mathbb{R}, $$
where L is not required to be either uniformly positive definite or coercive, and W is superquadratic at infinity in u but does not need to satisfy the Ambrosetti-Rabinowitz superquadratic condition.

Submitted December 14, 2015. Published March 10, 2016.
Math Subject Classifications: 34C37, 35A15, 37J45.
Key Words: Hamiltonian system; Homoclinic solution; variational method.

Show me the PDF file (262 KB), TEX file for this article.

Wei Jiang
Department of Mathematics
Jiangxi Normal University
Nanchang 330022, China
email: jiangweijw1991@163.com
Qingye Zhang
Department of Mathematics
Jiangxi Normal University
Nanchang 330022, China
email: qingyezhang@gmail.com

Return to the EJDE web page