Existence of solutions for p-Laplacian discrete equations

摘要

This work is devoted to the study of the existence of at least one (non-zero) solution to a problem involving the discrete p-Laplacian. As a special case, we derive an existence theorem for a second-order discrete problem, depending on a positive real parameter α, whose prototype is given by-Δ2u(k-1)=αf(k,u(k)),∀k∈Z[1,T],u(0)=u(T+1)=0.Our approach is based on variational methods in finite-dimensional setting.