Remarks on the Berestycki-Lions Conditions for the Existence of Solutions

In this paper, we are concerned with the following Schrodinger equation -Delta u=g(u),x is an element of Double-struck capital RN.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ - \Delta u = g(u),\,\,\,\,\,\,x \in {\mathbb{R}<^>N}.$$\end{document} We give a new approach and a brief proof to show the existence of infinitely many solutions and ground state solutions with g satisfying the Berestycki-Lions conditions [Arch. Rational Mech. Anal., 1983, 82(4): 313-345, 347-357].