Existence of Homoclinic Orbits for a Class of Asymptoticallyp-Linear Difference Systems withp-Laplacian

Abstract

By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptoticallyp-linear difference system withp-LaplacianΔ(|Δu(n-1)|p-2Δu(n-1))+∇[-K(n,u(n))+W(n,u(n))]=0, wherep∈(1,+∞),n∈ℤ,u∈ℝN,K,W:ℤ×ℝN→ℝare not periodic inn, and W is asymptoticallyp-linear at infinity.