Three solutions for a partial discrete Dirichlet boundary value problem with p-Laplacian

Boundary value problems

Zhan Zhou¹  Shaohong Wang¹ 

[1] School of Mathematics and Information Science, Guangzhou University, Guangzhou, P.R. China;Center for Applied Mathematics, Guangzhou University, Guangzhou, P.R. China;

关键词: Boundary value problem;    Partial difference equation;    Critical point theory;    p;   

DOI  :  10.1186/s13661-021-01514-9

来源: Springer

【 摘 要 】

By employing critical point theory, we investigate the existence of solutions to a boundary value problem for a p-Laplacian partial difference equation depending on a real parameter. To be specific, we give precise estimates of the parameter to guarantee that the considered problem possesses at least three solutions. Furthermore, based on a strong maximum principle, we show that two of the obtained solutions are positive under some suitable assumptions of the nonlinearity.

【 授权许可】

CC BY