Boundary value problems for a second-order difference equation involving the mean curvature operator

Abstract

Abstract In this paper, we consider the existence of multiple solutions for discrete boundary value problems involving the mean curvature operator by means of Clark’s Theorem, where the nonlinear terms do not need any asymptotic and superlinear conditions at 0 or at infinity. Further, the existence of a positive solution has been considered by the strong comparison principle. As an application, some examples are given to illustrate the obtained results.

Keywords

• Discrete boundary value problems
• Mean curvature operator
• Palais–Smale condition
• Critical-point theory