Periodic Solutions of Second Order Nonlinear Difference Equations with Singularϕ-Laplacian Operator

Abstract

We obtain some existence results of solutions for discrete periodic boundary value problems with singularϕ-Laplacian operator∇Δuk/1-κ(Δuk)2+rkuk+mk/(uk)λ=ek,  2≤k≤N-1,          u1=uN, and    Δu1=ΔuN-1by using the upper and lower solutions method and Brouwer degree theory, whereκ>0is a constant,r=(r2,…,rN-1),m=(m2,…,mN-1),e=(e2,…,eN-1)∈RN-2, andλ>0is a parameter. We also give some examples with singular nonlinearities to illustrate our main results.