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Research Article | Open Access

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

Chenghua Gao( ), Enming Yang, Huijuan Li
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
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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.

Keywords

discrete resonance problemeigenparameter-dependent boundary conditionsLyapunov-Schmidt methodexistencemultiplicity

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Electronic Research Archive
Volume 32 Issue 3,
March 2024
Pages 1692-1707
DOI: 10.3934/era.2024077

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Cite this article:
Gao C, Yang E, Li H. Solutions to a discrete resonance problem with eigenparameter-dependent boundary conditions. Electronic Research Archive, 2024, 32(3): 1692-1707. https://doi.org/10.3934/era.2024077

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Received: 11 September 2023
Revised: 03 February 2024
Accepted: 19 February 2024
Published: 26 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)