Ground state solutions for a class of elliptic Dirichlet problems involving the p(x)-Laplacian

被引：0

作者：

Bin Ge

Xiang-Wu Zhuge

Wen-Shuo Yuan

机构：

[1] Harbin Engineering University,College of Mathematical Sciences

来源：

Analysis and Mathematical Physics | 2021年 / 11卷

关键词：

(; )-Laplacian equation; Variable exponent Sobolev space; Ground state solutions; Multiple solutions; Nehari manifold; 35J60; 35J70; 35D30;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We are interested in the existence and multiplicity of ground state solutions for a class of p(x)-Laplacian Dirichlet problem in bounded domains. Firstly, combining constraint variational method and quantitative deformation lemma, we prove that the equation possesses at least one least energy sign-changing solution with exactly two nodal domains. Finally, using a strong maximum principle, we obtain three ground state solutions (one positive, one negative, and one sign-changing) for this problem.

引用

共 50 条

[1] Ground state solutions for a class of elliptic Dirichlet problems involving the p(x)-Laplacian
Ge, Bin
Zhuge, Xiang-Wu
Yuan, Wen-Shuo
ANALYSIS AND MATHEMATICAL PHYSICS, 2021, 11 (03)
[2] EXISTENCE OF THREE SOLUTIONS FOR ELLIPTIC DIRICHLET PROBLEMS INVOLVING THE p-LAPLACIAN
Afrouzi, G. A.
Hadjian, A.
Roushan, T. A.
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2014, 76 (01): : 79 - 86
[3] Existence results of infinitely many solutions for p(x)-Laplacian elliptic Dirichlet problems
Bonanno, Gabriele
Chinni, Antonia
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (11) : 1233 - 1246
[4] Discontinuous elliptic problems involving the p(x)-Laplacian
Bonanno, Gabriele
Chinni, Antonia
MATHEMATISCHE NACHRICHTEN, 2011, 284 (5-6) : 639 - 652
[5] Multiple solutions to a class of inclusion problems with operator involving p(x)-Laplacian
Zhou, Qingmei
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2013, (63) : 1 - 12
[6] POSITIVE SOLUTIONS FOR CONCAVE-CONVEX ELLIPTIC PROBLEMS INVOLVING p(x)-LAPLACIAN
Dammak, Makkia
Ben Ali, Abir Amor
Taarabti, Said
MATHEMATICA BOHEMICA, 2022, 147 (02): : 155 - 168
[7] Multiple solutions for inequality Dirichlet problems by the p(x)-Laplacian
Ge, Bin
Xue, Xiaoping
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (04) : 3198 - 3210
[8] Solutions for p(x)-Laplacian Dirichlet problems with singular coefficients
Fan, XL
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 312 (02) : 464 - 477
[9] Multiplicity of Positive Solutions for a Class of Inhomogeneous Neumann Problems Involving the p(x)-Laplacian
Xianling Fan
Shao-Gao Deng
Nonlinear Differential Equations and Applications NoDEA, 2009, 16 : 255 - 271
[10] Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian
Du, Sijia
Zhou, Zhan
MATHEMATICS, 2020, 8 (11) : 1 - 20

← 1 2 3 4 5 →