Results on multiple nontrivial solutions to partial difference equations-Reference-Cited by-同舟云学术

Results on multiple nontrivial solutions to partial difference equations

Published:2022 Issue:3 Volume:8 Page:5413-5431
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zhang Huan¹²,Zhou Yin³,Long Yuhua¹²

Affiliation:

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

2. Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou, 510006, China

3. Transportation and Economics Research Institute of China Academy of Railway Sciences Corporation Limited, Beijing, 100081, China

Abstract

<abstract><p>In this paper, we consider the existence and multiplicity of nontrivial solutions to second order partial difference equation with Dirichlet boundary conditions by Morse theory. Given suitable conditions, we establish multiple results that the problem admits at least two nontrivial solutions. Moreover, we provide five examples to illustrate applications of our theorems.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference26 articles.

1. J. S. Yu, J. Li, Discrete-time models for interactive wild and sterile mosquitoes with general time steps, Math. Biosci., 346 (2022), 108797. https://doi.org/10.1016/j.mbs.2022.108797

2. Y. H. Long, L. Wang, Global dynamics of a delayed two-patch discrete SIR disease model, Commun. Nonlinear Sci., 83 (2020), 105117. https://doi.org/10.1016/j.cnsns.2019.105117

3. Y. H. Long, Q. Q. Zhang, Sign-changing solutions of a discrete fourth-order Lidstone problem with three parameters, J. Appl. Anal. Comput., 12 (2022), 1118–1140. https://doi.org/10.11948/20220148

4. Y. H. Long, Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients, J. Differ. Equ. Appl., 26 (2020), 966–986. https://doi.org/10.1080/10236198.2020.1804557

5. Y. H. Long, Existence of two homoclinic solutions for a nonperiodic difference equation with a perturbation, AIMS Math., 6 (2021), 4786–4802. https://doi.org/10.3934/math.2021281

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