On the existence of multiple solutions for a partial discrete Dirichlet boundary value problem with mean curvature operator

Abstract

Apartial discrete Dirichlet boundary value problem involving mean curvature operator is concerned in this paper. Under proper assumptions on the nonlinear term, we obtain some feasible conditions on the existence of multiple solutions by the method of critical point theory. We further separately determine open intervals of the parameter to attain at least two positive solutions and an unbounded sequence of positive solutions with the help of the maximum principle.

Keywords

• partial difference equations
• boundary value problem
• mean curvature operator
• multiple solutions
• critical point theory
• 39a14
• 39a70