Results on multiple nontrivial solutions to partial difference equations

AIMS Mathematics

article

Huan Zhang¹  Yin Zhou³  Yuhua Long¹ 

[1] School of Mathematics and Information Science, Guangzhou University;Guangzhou University, Guangzhou Center for Applied Mathematics;Transportation and Economics Research Institute of China Academy of Railway Sciences Corporation Limited

关键词: partial difference equation;    local linking;    Morse theory;    nontrivial solution;   

DOI  :  10.3934/math.2023272

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY