Multiple homoclinic orbits for a class of second order perturbed Hamiltonian systems (Q1422592)

The author studies Hamiltonian systems of the form \(-q''=W_q(t,q),\) where \(W_q\) is the gradient of \(W\). He extends the class of functions \(W\) considered by \textit{W. Omana} and \textit{M. Willem} [Differ. Integral Equ. 5, 1115--1120 (1992; Zbl 0759.58018)] and proves for this extended class the existence of an infinite family of solutions \(q(t)\) such that \(| q(t)| \to 0\) and \(| q'(t)| \to 0\) as \(| t| \to\infty\).