Infinitely many sign-changing solutions for p-Laplacian Neumann problems with indefinite weight

被引：8

作者：

He, Tieshan ^{[1
]}

Chen, Chuanyong ^{[1
]}

Huang, Yehui ^{[1
]}

Hou, Chaojun ^{[1
]}

机构：

[1] Zhongkai Univ Agr & Engn, Coll Computat Sci, Guangzhou 510225, Guangdong, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2015年 / 39卷

关键词：

p-Laplacian; Sign-changing solution; Critical point theory; Indefinite potential; Truncation; ELLIPTIC-EQUATIONS; MULTIPLICITY; EXISTENCE; THEOREM;

D O I：

10.1016/j.aml.2014.08.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider nonlinear Neumann problems driven by p-Laplacian plus an indefinite potential. Using critical point theory, coupled with suitable truncation techniques, we show that the problem has infinitely many sign-changing solutions. The interesting point is that we do not impose any restrictions to the behavior of the reaction term f at infinity. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：73 / 79

页数：7

共 23 条

[1] Existence of multiple solutions with precise sign information for superlinear Neumann problems [J].

Aizicovici, Sergiu ;

Papageorgiou, Nikolaos S. ;

Staicu, Vasile .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2009, 188 (04) :679-715

[2] Existence of infinitely many weak solutions for a Neumann problem [J].

Anello, G .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 57 (02) :199-209

[3] Existence and multiplicity results to Neumann problems for elliptic equations involving the p-Laplacian [J].

Bonanno, Gabriele ;

Sciammetta, Angela .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 390 (01) :59-67

[4] Multiplicity results for a Neumann problem involving the p-Laplacian [J].

Faraci, F .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 277 (01) :180-189

[5]

Gasinski L., 2006, Ser. Math. Anal. Appl., V9

[6] MULTIPLE SOLUTIONS FOR A CLASS OF NONLINEAR NEUMANN EIGENVALUE PROBLEMS [J].

Gasinski, Leszek ;

Papageorgiou, Nikolaos S. .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (04) :1491-1512

[7] Existence and uniqueness of positive solutions for the Neumann p-Laplacian [J].

Gasinski, Leszek ;

Papageorgiou, Nikolaos S. .

POSITIVITY, 2013, 17 (02) :309-332

[8] A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations [J].

Kajikiya, R .

JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 225 (02) :352-370

[9] BOUNDARY-REGULARITY FOR SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

LIEBERMAN, GM .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1988, 12 (11) :1203-1219

[10] Multiple existence results of solutions for the Neumann problems via super- and sub-solutions [J].

Miyajima, Shizuo ;

Motreanu, Dumitru ;

Tanaka, Mieko .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (04) :1921-1953

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