Multiple solutions for semi-linear corner degenerate elliptic equations with singular potential term

被引：2

作者：

Chen, Hua ^{[1
]}

Tian, Shuying ^{[1
,2
]}

Wei, Yawei ^{[3
,4
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Wuhan Univ Technol, Sch Sci, Wuhan 430070, Peoples R China

[3] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[4] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2017年 / 19卷 / 04期

关键词：

Corner-degenerate elliptic operator; multiple solutions; singular potential term; weighted corner type Hardy inequality;

D O I：

10.1142/S0219199716500437

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present paper is concern with the Dirichlet problem for semi-linear corner degenerate elliptic equations with singular potential term. We first give the preliminary of the framework and then discuss the weighted corner type Hardy inequality. By using the variational method, we prove the existence of multiple solutions for the Dirichlet boundary-value problem.

引用

页数：17

共 18 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2]

Ambrosetti A., 2012, CALC VAR PARTIAL DIF, V43, P463

[3]

[Anonymous], 1991, COMMUNICATIONS PARTI

[4] Multiple sign changing solutions for semi-linear corner degenerate elliptic equations with singular potential [J].

Chen, Hua ;

Tian, Shuying ;

Wei, Yawei .

JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 270 (04) :1602-1621

[5] Multiple solutions for semi-linear corner degenerate elliptic equations [J].

Chen, Hua ;

Liu, Xiaochun ;

Wei, Yawei .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (06) :3815-3839

[6] Existence of solutions for degenerate elliptic equations with singular potential on conical singular manifolds [J].

Chen, Hua ;

Wei, Yawei ;

Zhou, Bin .

MATHEMATISCHE NACHRICHTEN, 2012, 285 (11-12) :1370-1384

[7] Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term [J].

Chen, Hua ;

Liu, Xiaochun ;

Wei, Yawei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (07) :4289-4314

[8] Multiple solutions for semilinear totally characteristic elliptic equations with subcritical or critical cone Sobolev exponents [J].

Chen, Hua ;

Liu, Xiaochun ;

Wei, Yawei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (07) :4200-4228

[9] Existence theorem for a class of semilinear totally characteristic elliptic equations with critical cone Sobolev exponents [J].

Chen, Hua ;

Liu, Xiaochun ;

Wei, Yawei .

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2011, 39 (01) :27-43

[10]

Egorov Ju. V., 1997, OPERATOR THEORY ADV, V93

← 1 2 →