Nonexistence and existence results for a 2 $$n$$ n th-order discrete mixed boundary value problem

Abstract

In this paper, a 2\(n\)th-order nonlinear difference equation is considered. By using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for mixed boundary value problem and give some new results. Recent results in the literature are generalized and significantly complemented.