Solutions to a discrete resonance problem with eigenparameter-dependent boundary conditions

Abstract

In this paper, we considered the existence of solutions to a discrete second-order resonance problem with eigenparameter-dependent boundary conditions. We first transformed the resonance problem into its corresponding equivalent system using the Lyapunov-Schmidt method. In addition, using Schauder's fixed-point theorem and the connectivity theories of the solution set of compact vector fields, we obtained the existence and multiplicity of solutions to the second-order discrete resonance problem with eigenparameter-dependent boundary conditions.

Keywords

• discrete resonance problem
• eigenparameter-dependent boundary conditions
• lyapunov-schmidt method
• existence
• multiplicity