Homoclinic solutions for a semilinear elliptic equation with an asymptotically linear nonlinearity

We study the following semilinear elliptic equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\Delta u + b(x)u = f(u), \ \ \ x\in{\mathbf R}^N, $$\end{document} where b is periodic and f is assumed to be asymptotically linear. The purpose of this paper is to establish the existence of infinitely many homoclinic type solutions for this class of nonlinearities.