On Existence of Infinitely Many Homoclinic Solutions

 In this note we prove some sufficient condition for the existence of homoclinic solutions in nonautonomous ODE’s. As an application we show that there exist infinitely many (geometrically distinct) homoclinic solutions to the trivial 0 solution in the planar system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}