Multiplicity of positive solutions for a class of quasilinear nonhomogeneous Neumann problems

被引：27
作者：
Abreu, EAM
do O, JM [1 ]
Medeiros, ES
机构：
[1] Univ Fed Paraiba, Dept Matemat, BR-58059900 Joao Pessoa, Paraiba, Brazil
[2] Univ Fed Minas Gerais, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 60卷 / 08期
关键词：
nonlinear elliptic problems; Neumann boundary value problems; positive solutions; lower and upper; solutions; variational methods; p-Laplacian; critical exponent;
D O I：
10.1016/j.na.2004.09.058
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the existence, nonexistence and multiplicity of positive solutions for nonhomogeneous Neumann boundary value problem of the type { -Delta(p)u + lambdau(p-1) = u(q) in Omega, {u > 0 in Omega, {\delu\(p-2) partial derivativeu/partial derivativen=phi on partial derivativeOmega where Omega is a bounded domain in R-n with smooth boundary, 1 < p < n, Delta(P)u = div(\delu\(p-2)delu) is the p-Laplacian operator, p - 1 < q less than or equal to p* - 1, p* = np/(n - p), phi is an element of C-alpha (Omega), 0 < alpha < 1, phi not equivalent to 0, (x) greater than or equal to 0 and lambda is a real parameter. The proofs of our main results rely on different methods: lower and upper solutions and variational approach. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1443 / 1471
页数：29
相关论文
共 18 条
[11]   QUASILINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].
GUEDDA, M ;
VERON, L .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1989, 13 (08) :879-902
[12]   BOUNDARY-REGULARITY FOR SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].
LIEBERMAN, GM .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1988, 12 (11) :1203-1219
[13]   ON A NEUMANN PROBLEM WITH CRITICAL EXPONENT AND CRITICAL NONLINEARITY ON THE BOUNDARY [J].
PIEROTTI, D ;
TERRACINI, S .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (5-6) :1043-1075
[14]   A HARNACK INEQUALITY FOR NONLINEAR EQUATIONS [J].
SERRIN, J .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1963, 69 (04) :481-&
[15]   ON THE DIRICHLET-PROBLEM FOR QUASILINEAR EQUATIONS IN DOMAINS WITH CONICAL BOUNDARY POINTS [J].
TOLKSDORF, P .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1983, 8 (07) :773-817
[16]   ON HARNACK TYPE INEQUALITIES AND THEIR APPLICATION TO QUASILINEAR ELLIPTIC EQUATIONS [J].
TRUDINGER, NS .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1967, 20 (04) :721-+
[17]   NEUMANN PROBLEMS OF SEMILINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].
WANG, XJ .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 93 (02) :283-310
[18]  
Willem M., 1996, Minimax theorems, V24
12