Fast and slow decay solutions for supercritical elliptic problems in exterior domains

被引：42

作者：

Davila, Juan ^{[2
,3
]}

del Pino, Manuel ^{[2
,3
]}

Musso, Monica ^{[4
,5
]}

Wei, Juncheng ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

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

[3] Univ Chile, CMM, Santiago, Chile

[4] Pontificia Univ Catolica Chile, Dept Matemat, Macul 4860, Chile

[5] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 32卷 / 04期

关键词：

D O I：

10.1007/s00526-007-0154-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the elliptic problem Delta u + u(p) = 0, u > 0 in an exterior domain, Omega = R(N)\D under zero Dirichlet and vanishing conditions, where D is smooth and bounded in R(N), N >= 3, and p is supercritical, namely p > N+2/N-2. We prove that this problem has infinitely many solutions with slow decay O(vertical bar x vertical bar(-2/p-1)) at infinity. In addition, a solution with fast decay O(vertical bar x vertical bar(2- N)) exists if p is close enough from above to the critical exponent.

引用

页码：453 / 480

页数：28

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