Non-trivial solutions for a partial discrete Dirichlet nonlinear problem with p-Laplacian

被引：5

作者：

He, Huiting ^{[1
]}

Ousbika, Mohamed ^{[2
]}

El Allali, Zakaria ^{[2
]}

Zuo, Jiabin ^{[1
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[2] Univ Mohammed First Oujda, Fac Multidisciplinary Nador, Oriental Appl Math Lab, Team Modeling & Sci Comp, Oujda, Morocco

来源：

COMMUNICATIONS IN ANALYSIS AND MECHANICS | 2023年 / 15卷 / 04期

基金：

中国博士后科学基金;

关键词：

partial discrete nonlinear problem; critical point theory; p-Laplacian; non-trivial solutions; BOUNDARY-VALUE PROBLEM; MULTIPLE SOLUTIONS; EXISTENCE; OPERATOR;

D O I：

10.3934/cam.2023030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the non-trivial solutions for a partial discrete Dirichlet nonlinear problem with p-Laplacian by applying Ricceri's variational principle and a two non-zero critical points theorem. In addition, we identify open intervals of the parameter lambda under appropriate constraints imposed on the nonlinear term. This allows us to ensure that the nonlinear problem has at least one or two non-trivial solutions.

引用

页码：598 / 610

页数：13

共 22 条

[1] Two Non-Zero Solutions for Elliptic Dirichlet Problems [J].

Bonanno, Gabriele ;

D'Agui, Giuseppina .

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2016, 35 (04) :449-464

[2] A critical point theorem via the Ekeland variational principle [J].

Bonanno, Gabriele .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (05) :2992-3007

[3] Bounded solutions to systems of fractional discrete equations [J].

Diblik, Josef .

ADVANCES IN NONLINEAR ANALYSIS, 2022, 11 (01) :1614-1630

[4] On the existence of multiple solutions for a partial discrete Dirichlet boundary value problem with mean curvature operator [J].

Du, Sijia ;

Zhou, Zhan .

ADVANCES IN NONLINEAR ANALYSIS, 2022, 11 (01) :198-211

[5] Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian [J].

Du, Sijia ;

Zhou, Zhan .

MATHEMATICS, 2020, 8 (11) :1-20

[6] SPECTRUM OF DISCRETE 2n-TH ORDER DIFFERENCE OPERATOR WITH PERIODIC BOUNDARY CONDITIONS AND ITS APPLICATIONS [J].

El Amrouss, Abdelrachid ;

Hammouti, Omar .

OPUSCULA MATHEMATICA, 2021, 41 (04) :489-507

[7] On the existence of solutions for discrete elliptic boundary value problems [J].

Galewski, Marek ;

Orpel, Aleksandra .

APPLICABLE ANALYSIS, 2010, 89 (12) :1879-1891

[8] The existence of periodic and subharmonic solutions of subquadratic second order difference equations [J].

Guo, ZM ;

Yu, JS .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2003, 68 :419-430

[9] NONTRIVIAL SOLUTIONS FOR PARTIAL DISCRETE DIRICHLET PROBLEMS VIA A LOCAL MINIMUM THEOREM FOR FUNCTIONALS [J].

Heidarkhani, Shapour ;

Imbesi, Maurizio .

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2019, 2019

[10] Multiple solutions for partial discrete Dirichlet problems depending on a real parameter [J].

Heidarkhani, Shapour ;

Imbesi, Maurizio .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2015, 21 (02) :96-110

← 1 2 3 →