Three solutions for a discrete fourth-order boundary value problem with four parameters

Abstract

This paper presents several sufficient conditions for the existence of at least three classical solutions of a boundary value problem for a fourth-order difference equation. Fourth-order boundary value problems act as models for the bending or deforming of elastic beams. In different fields of research, such as computer science, mechanical engineering, control systems, artificial or biological neural networks, economics and many others, the mathematical modelling of important questions leads naturally to the consideration of nonlinear difference equations. Our technical approach is based on variational methods. An example is included in the paper. Numerical computations of the example confirm our theoretical results.