Unbounded perturbations of nonlinear discrete periodic problem at resonance Original Research Article

In this paper, we study the existence of solutions of nonlinear discrete boundary value problems View the MathML source{Δ2u(t−1)+λku(t)+g(t,u(t))=h(t),u(0)=u(T),u(1)=u(T+1), Turn MathJax on where T≔{1,…,T}T≔{1,…,T}, h:T→Rh:T→R, λkλk is the kk-th eigenvalue of the linear problem View the MathML source{Δ2u(t−1)+λu(t)=0,u(0)=u(T),u(1)=u(T+1), Turn MathJax on g:N×R→Rg:N×R→R satisfies some ‘asymptotic nonuniform’ resonance conditions, and g(t,u)u≥0g(t,u)u≥0 for u∈Ru∈R.