Homoclinic solutions for nonlinear general fourth order differential equations

Abstract

This work provides su¢ cient conditions for the existence of homoclinic solutions of fourth-order nonlinear ordinary di¤erential equations. Us- ing the Green s functions, we formulate a new modi ed integral equa- tion which is equivalent to the original nonlinear equation. In an adequate function space, the corresponding nonlinear integral opera- tor is compact, and it is proved an existence result by Schauder s xed point theorem .