Three solutions to Dirichlet problems for second-order self-adjoint difference equations involving p -Laplacian

Advances in Difference Equations

article

Xiong, Feng¹  Zhou, Zhan¹ 

[1] School of Mathematics and Information Sciences, Guangzhou University;Center for Applied Mathematics, Guangzhou University

关键词: Three solutions;    p -Laplacian;    Self-adjoint;    Boundary value problem;    Critical point theory;   

DOI  :  10.1186/s13662-021-03350-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper derives several sufficient conditions for the existence of three solutions to the Dirichlet problem for a second-order self-adjoint difference equation involving p-Laplacian through the critical point theory. Furthermore, by using the strong maximum principle, we prove that the three solutions are positive under appropriate assumptions on the nonlinearity. Finally, we present three examples to confirm our results.

【 授权许可】

CC BY