Existence of Homoclinic Orbits for a Singular Differential Equation Involving p-Laplacian

Abstract EN

The efficient conditions guaranteeing the existence of homoclinic solutions to second-order singular differential equation with p-Laplacian ϕpx′t′+fx′t+gxt+ht/1−xt=et are established in the paper.

Here, ϕps=sp−2s,p>1,f,g,h,e∈Cℝ,ℝ with ht+T=ht.

The approach is based on the continuation theorem for coincidence degree theory.