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

被引：18

作者：

Wang, Shaohong ^{[1
,2
]}

Zhou, Zhan ^{[1
,2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Peoples R China

[2] Guangzhou Univ, Ctr Appl Math, Guangzhou, Peoples R China

来源：

BOUNDARY VALUE PROBLEMS | 2021年 / 2021卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Boundary value problem; Partial difference equation; Critical point theory; p-Laplacian; NONLINEAR DIFFERENCE-EQUATIONS; HOMOCLINIC SOLUTIONS; SUBHARMONIC SOLUTIONS; MULTIPLE SOLUTIONS; POSITIVE SOLUTIONS; EXISTENCE; ADVANCE; ORBITS;

D O I：

10.1186/s13661-021-01514-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：17

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