A Palais-Smale approach to Lane-Emden equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:330

Article

Lin, Huei-li ; Wang, Weichung

关键词: Palais-Smale sequences;    Palais-Smale values;    Palais-Smale conditions;    Lane-Emden equations;    unbounded domain;    stretched interior flask domain;   

DOI  :  10.1016/j.jmaa.2006.08.023

来源: Elsevier

【 摘 要 】

We consider the unbounded domain problems -Delta u + u = vertical bar u vertical bar(p-2)u in Omega, u > 0 in Omega, and u = 0 on delta Omega, where Omega is an unbounded domain in R-N, 2 < p < 2*, 2* = 2N/N-2 for N > 2, and 2* = infinity for N = 2. The existence of a ground state solution to the problems is greatly affected by the shape of the domain. To determine the existence of the solutions in a general domain remains a challenge task. For the flat interior flask domain that consists a strip and a ball attached to the bottom of the strip, previous results have asserted the existence of a ground state solution when the diameter of the ball is greater than a positive constant. However, the existence of the solutions when the diameter of the ball equals to the width of the strip is still an important open question. This article resolves the open question partially by considering a variation of the flat interior flask domain, which is formed by attaching a stretched ball to the bottom of the strip. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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