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

Chenghua Gao; Enming Yang; Huijuan Li; Chenghua Gao; Enming Yang; Huijuan Li

doi:10.3934/era.2024077

Electronic Research Archive

2024, Volume 32, Issue 3: 1692-1707. doi: 10.3934/era.2024077

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Research article

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

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Academic Editor: Shuang Miao

Received: 11 September 2023 Revised: 03 February 2024 Accepted: 19 February 2024 Published: 26 February 2024

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.
- discrete resonance problem,
- eigenparameter-dependent boundary conditions,
- Lyapunov-Schmidt method,
- existence,
- multiplicity
Citation: Chenghua Gao, Enming Yang, Huijuan Li. Solutions to a discrete resonance problem with eigenparameter-dependent boundary conditions[J]. Electronic Research Archive, 2024, 32(3): 1692-1707. doi: 10.3934/era.2024077

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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.

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