Boundary Value Problems
Volume 2009 (2009), Article ID 959636, 21 pages
doi:10.1155/2009/959636

Homoclinic solutions of singular nonautonomous second-order differential equations

Abstract

This paper investigates the singular differential equation (p(t)u′)′=p(t)f(u), having a singularity at t=0. The existence of a strictly increasing solution (a homoclinic solution) satisfying u′(0)=0, u(∞)=L>0 is proved provided that f has two zeros and a linear behaviour near −∞.