Existence of Three Solutions for a Nonlinear Discrete Boundary Value Problem with <i>ϕ_c</i>-Laplacian

Abstract

In this paper, based on critical point theory, we mainly focus on the multiplicity of nontrivial solutions for a nonlinear discrete Dirichlet boundary value problem involving the mean curvature operator. Without imposing the symmetry or oscillating behavior at infinity on the nonlinear term f, we respectively obtain the sufficient conditions for the existence of at least three non-trivial solutions and the existence of at least two non-trivial solutions under different assumptions on f. In addition, by using the maximum principle, we also deduce the existence of at least three positive solutions from our conclusion. As far as we know, our results are supplements to some well-known ones.

Keywords

• <i>ϕ_c</i>-Laplacian
• boundary value problem
• critical point theory
• three solutions