Infinitely Many Solutions for the Discrete Boundary Value Problems of the Kirchhoff Type

Abstract

In this paper, we study the existence and multiplicity of solutions for the discrete Dirichlet boundary value problem of the Kirchhoff type, which has a symmetric structure. By using the critical point theory, we establish the existence of infinitely many solutions under appropriate assumptions on the nonlinear term. Moreover, we obtain the existence of infinitely many positive solutions via the strong maximum principle. Finally, we take two examples to verify our results.

Keywords

• discrete Kirchhoff-type problem
• boundary value problems
• infinitely many solutions
• critical point theory