Existence of nonnegative solutions for quasilinear elliptic equations with indefinite critical nonlinearities

被引：3

作者：

Narukawa, Kimiaki ^{[1
]}

Takajo, Yukihiro ^{[1
]}

机构：

[1] Naruto Univ Educ, Dept Math, Naruto 7728502, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 16期

基金：

日本学术振兴会;

关键词：

Quasilinear elliptic equation; Nonnegative solution; Critical exponent; Indefinite coefficients; CRITICAL SOBOLEV EXPONENTS; POSITIVE SOLUTIONS; R-N; LOCAL SUPERLINEARITY; CRITICAL GROWTH; P-LAPLACIAN; SUBLINEARITY;

D O I：

10.1016/j.na.2011.05.071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the quasilinear elliptic equation -div(phi(vertical bar del u vertical bar)del u) = a(x) f (u) + b(x) g(u) in Omega with Dirichlet boundary condition u = 0 on partial derivative Omega, where Omega is a bounded domain in R(N), a(x), b(x) are sign-changing continuous functions, and g(u) has critical growth at infinity with respect to the principal part phi. A nonnegative, nontrivial solution is given under appropriate growth conditions on f (u), g(u) at 0 and infinity. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：5793 / 5813

页数：21

共 18 条

[1] COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS
AMBROSETTI, A
BREZIS, H
CERAMI, G
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) : 519 - 543
[2] Elliptic variational problems in RN with critical growth
Ambrosetti, A
Azorero, JG
Peral, I
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 168 (01) : 10 - 32
[3] [Anonymous], 2003, SOBOLEV SPACES
[4] SOME RESULTS ABOUT THE EXISTENCE OF A 2ND POSITIVE SOLUTION IN A QUASI-LINEAR CRITICAL PROBLEM
AZORERO, JG
ALONSO, IP
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1994, 43 (03) : 941 - 957
[5] An eigenvalue problem for a quasilinear elliptic field equation
Benci, V
Micheletti, AM
Visetti, D
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 184 (02) : 299 - 320
[6] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
BREZIS, H
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) : 437 - 477
[7] On the stationary solutions of generalized reaction diffusion equations with p&q-Laplacian
Cherfils, L
Il'Yasov, Y
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2005, 4 (01) : 9 - 22
[8] Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems
Dal Maso, G
Murat, F
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 31 (3-4) : 405 - 412
[9] de Figueiredo DG, 2006, J EUR MATH SOC, V8, P269
[10] Local "superlinearity" and "sublinearity" for the p-Laplacian
de Figueiredo, Djairo G.
Gossez, Jean-Pierre
Ubilla, Pedro
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 257 (03) : 721 - 752

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