THE EFFECT OF DIFFUSION ON CRITICAL QUASILINEAR ELLIPTIC PROBLEMS

被引：0

作者：

de Moura, Renato Jose ^{[1
]}

Montenegro, Marcos ^{[2
]}

机构：

[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil

[2] Univ Fed Minas Gerais, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2014年 / 43卷 / 02期

关键词：

Non-uniformly elliptic operators; critical Sobolev exponent; best constant; Hardy-Sobolev inequality; CRITICAL SOBOLEV EXPONENTS; POSITIVE SOLUTIONS; P-LAPLACIAN; EQUATIONS; EXISTENCE; INEQUALITIES; NONLINEARITIES; COMPACTNESS; IDENTITY; DOMAINS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the role of the diffusion coefficient a(x) on the existence of a positive solution for the quasilinear elliptic problem involving critical exponent [GRAPHICS] where Omega is a smooth bounded domain in R-n, n >= 2, 1 < p < n, p* = np/(n-p) is the critical exponent from the viewpoint of Sobolev embedding, lambda is a real parameter and a:(Omega) over bar -> R is a positive continuous function. We prove that if the function a(x) has an interior global minimum point x(0) of order sigma, then the range of values lambda for which the problem above has a positive solution relies strongly on sigma. We discover in particular that the picture changes drastically from sigma > p to sigma <= p. Some sharp answers are also provided.

引用

页码：517 / 534

页数：18

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