Pairs of positive solutions for singular p-Laplacian equations with a p-superlinear potential

被引：11

作者：

Kyritsi, Sophia Th. ^{[2
]}

Papageorgiou, Nikolaos S. ^{[1
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

[2] Hellen Naval Acad, Dept Math, Piraeus 18539, Greece

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 05期

关键词：

Singular equation; p-Laplacian; C-condition; Upper and lower solutions; p-superlinear term; Mountain pass theorem; EXISTENCE; SIGN;

D O I：

10.1016/j.na.2010.04.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a singular parametric elliptic equation driven by the p-Laplacian and with a p-superlinear potential which does not satisfy the Ambrosetti-Rabinowitz condition. Using variational arguments, combined with truncation techniques and the method of upper and lower solutions, we show that there exists a lambda* > 0 such that if the parameter lambda is in (0, lambda*), then the problem has two ordered smooth positive strong solutions. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1136 / 1142

页数：7

共 14 条

[1] Singular initial and boundary value problems with sign changing nonlinearities [J].

Agarwal, RP ;

O'Regan, D .

IMA JOURNAL OF APPLIED MATHEMATICS, 2000, 65 (02) :173-198

[2] Existence theorems for the one-dimensional singular p -: Laplacian equation with sign changing nonlinearities [J].

Agarwal, RP ;

Lü, HS ;

O'Regan, D .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 143 (01) :15-38

[3]

[Anonymous], 2010, Appl. Anal, DOI DOI 10.1080/00036810500474655

[4]

COCLITE MM, 1977, COMMUN PART DIFF EQ, V2, P193

[5] EXISTENCE RESULTS FOR PERTURBATIONS OF THE P-LAPLACIAN [J].

COSTA, DG ;

MAGALHAES, CA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 24 (03) :409-418

[6]

Gasinski L., 2006, NONLINEAR ANAL

[7] Classical and weak solutions of a singular semilinear elliptic problem [J].

Lair, AV ;

Shaker, AW .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 211 (02) :371-385

[8] A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations [J].

Motreanu, D. ;

Motreanu, V. V. ;

Papageorgiou, N. S. .

MANUSCRIPTA MATHEMATICA, 2007, 124 (04) :507-531

[9] Existence and multiplicity of positive solutions for singular quasilinear problems [J].

Perera, Kanishka ;

Silva, Elves A. B. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (02) :1238-1252

[10] Multiple positive solutions of singular p-Laplacian problems by variational methods [J].

Perera, Kanishka ;

Zhang, Zhitao .

BOUNDARY VALUE PROBLEMS, 2005, 2005 (03) :377-382

← 1 2 →