Fast and slow decay solutions for supercritical elliptic problems in exterior domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Juan Dávila Manuel del Pino Monica Musso Juncheng Wei

Affiliation:	1.Departamento de Ingeniería Matemática and CMM,Universidad de Chile,Santiago,Chile;2.Departamento de Matemática,Pontificia Universidad Católica de Chile,Macul,Chile;3.Dipartimento di Matematica,Politecnico di Torino,Torino,Italy;4.Department of Mathematics,Chinese University of Hong Kong,Shatin,Hong Kong

Abstract:	We consider the elliptic problem Δu + u ^p = 0, u > 0 in an exterior domain, ${Omega = mathbb{R}^N{setminus}mathcal{D}}$ under zero Dirichlet and vanishing conditions, where is smooth and bounded in ${mathbb{R}^N}$ , N ≥ 3, and p is supercritical, namely ${p > frac{N+2}{N-2}}$ . We prove that this problem has infinitely many solutions with slow decay ${O(\|x\|^{-frac2{p-1}})}$ at infinity. In addition, a solution with fast decay O(\|x\|^2-N) exists if p is close enough from above to the critical exponent.

Keywords:	KeywordHeading" >Mathematics Subject Classification (2000) 35J60 35B20 35B33 35J20
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