Quasilinear elliptic systems with critical Sobolev exponents in RN

被引：29

作者：

Djellit, Ali ^{[1
]}

Tas, Saadia ^{[1
]}

机构：

[1] Univ Annaba, Fac Sci, Dept Math, Annaba 23000, Algeria

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 66卷 / 07期

关键词：

p-Laplacian operator; critical Sobolev exponent; Palais-Smale condition; Mountain Pass Theorem; concentration-compactness principle;

D O I：

10.1016/j.na.2006.02.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study here a class of quasilinear elliptic systems involving the p-Laplacian operator; the right hand sides of systems are closely related to the critical Sobolev exponents. Under some additional assumptions on the nonlinearities, the corresponding functional verifies the Palais-Smale condition (PS)(c) for c belonging to a specified range. So, we can use the Mountain Pass Theorem to prove the existence of at least one nontrivial solution. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：1485 / 1497

页数：13

共 20 条

[1]

Allegretto W., 1995, FUNKC EKVACIOJ-SER I, V38, P233

[2]

Amster P, 2002, ELECTRON J DIFFER EQ

[3]

BERGER SM, 1977, NONLINEARITY FUNCTIO

[4] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[5] Some existence results for a class of nonlinear equations involving a duality mapping [J].

Dinca, G ;

Jebelean, P .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 46 (03) :347-363

[6] On some nonlinear elliptic systems [J].

Djellit, A ;

Tas, S .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 59 (05) :695-706

[7]

Djellit A., 2003, ELECT J DIFFERENTIAL, V2003, P1

[8] Multiplicity of positive solutions for some quasilinear elliptic equation in R-N with critical Sobolev exponent [J].

Drabek, P ;

Huang, YX .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 140 (01) :106-132

[9] NONLINEAR EIGENVALUE PROBLEM FOR P-LAPLACIAN IN R(N) [J].

DRABEK, P .

MATHEMATISCHE NACHRICHTEN, 1995, 173 :131-139

[10]

Kavian O., 1993, Introduction a la theorie des points critiques et applications aux problemes elliptiques, Mathematiques and Applications

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