Periodic solutions of second order nonlinear difference systems with [formula omitted]-Laplacian: A variational approach

Abstract

T-periodic solutions of systems of difference equations of the form Δϕ[Δu(n−1)]=∇uF[n,u(n)]+h(n)(n∈Z) where ϕ=∇Φ, Φ strictly convex, is a homeomorphism of RN onto the ball Ba⊂RN, or of Ba onto RN, are considered under various conditions upon F and h. The approach is variational.