Radial solutions of an elliptic equation with singular nonlinearity

被引：8

作者：

Davila, Juan ^{[1
,2
]}

Montenegro, Marcelo ^{[3
]}

机构：

[1] Univ Chile, Dept Ingn Matemat, Santiago, Chile

[2] CMM, Santiago, Chile

[3] Univ Estadual Campinas, IMECC, Dept Matemat, BR-13083970 Campinas, SP, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 352卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Radial solutions; Uniqueness; Singular nonlinearity; GROUND-STATES; DELTA-U; UNIQUENESS; DELTA-U+F(U)=0; RN;

D O I：

10.1016/j.jmaa.2008.05.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the equation -Delta u + u(-beta) = u(p), u > 0 in B-R, u = 0 on partial derivative B-R, where B-R subset of R-N, 0 < beta < 1 and 1 < p < N+2/N-2 if N >= 3, 1 < p < +infinity if N = 2, we show that there is (R) over bar > 0 such that a radial solution u(R) exists if and only if 0 < R <= <(R)over bar>. It is unique in the class of radial solutions and u(R)' (R) < 0 if R < (R) over bar, while u((R) over bar)'((R) over bar) = 0. We also give a variational characterization of u((R) over bar). (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：360 / 379

页数：20

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