Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

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 ∞.