# Even homoclinic solutions for a class of second order Hamiltonian systems

## Abstract

In this work we prove the existence of a nontrivial even homoclinic solution for second order time-dependent Hamiltonian systems with symmetric potentials $\ddot{x}(t)+V'(t,x(t))=0,$ where $t\in \mathbb{R},$ $ x\in\mathbb{R}^{N}$ and $V\in C^{1}(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R}),$ $ V(t,x)=-K(t,x)+W(t,x),$ under a kind of new superquadratic conditions. A homoclinic orbit is obtained as a limit of solutions of a certain sequence of boundary value problems which are obtained by the minimax methods.## Published

08/25/2010

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Articles