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

Abstract EN

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

We also give some examples with singular nonlinearities to illustrate our main results.