Multiple solutions of fourth-order difference equations with different boundary conditions

Abstract

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

Keywords

• Multiple solutions
• Boundary value problems
• Invariant sets of descending flow
• Mountain pass lemma