Homoclinic orbits for the second-order Hamiltonian systems with obstacle item

This paper is concerned with the existence of homoclinic orbits for the second-order Hamiltonian system with obstacle item, ü(t) − A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \dot u $$\end{document} (t) = ∇F(t, u), where F(t, u) is T-periodic in t with ∇F(t, u) = L(t)u + ∇R(t, u). By using a generalized linking theorem for strongly indefinite functionals, we prove the existence of homoclinic orbits for both the super-quadratic case and the asymptotically linear one.