Ground state solutions of a critical problem involving cylindrical weights

被引：34

作者：

Musina, Roberta ^{[1
]}

机构：

[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 12期

关键词：

variational methods; critical growth; weighted Hardy-Sobolev inequalities;

D O I：

10.1016/j.na.2007.04.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove some existence and non-existence results for a nonlinear elliptic equation involving cylindrical weights and critical growth. More precisely, defining xi = (x, y) epsilon R-k x RN-k, we study the variational problem {-div(vertical bar x vertical bar(a)del u) = lambda vertical bar x vertical bar(a-2)u + vertical bar x vertical bar(-b)u(p-1) in R-N, x not equal 0 u >= 0 under suitable assumptions for the parameters p epsilon (2, 2*) and a, lambda, b epsilon R. We firstly consider the strongly elliptic case a = 0. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：3972 / 3986

页数：15

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