Solutions of the mixed boundary problem and their Morse indices

被引：13
|
作者：
Yu, Xiaohui [1 ]
机构：
[1] Shenzhen Univ, Inst Adv Study, Shenzhen 518060, Guangdong, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 96卷
关键词：
Liouville type theorem; Morse index; Blowup; Mixed boundary; SUPERLINEAR ELLIPTIC-EQUATIONS;
D O I：
10.1016/j.na.2013.11.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the solutions of the following mixed boundary problem {-Delta u = f(x, u) in Omega, u = 0 on Sigma(1), partial derivative u/partial derivative nu = 0 on Sigma(2). Under some assumptions on the nonlinearity, we will show that the boundedness of solutions is equivalent to the finiteness of their Morse indices. We extend the result of A. Bahri, P.L. Lions, Solutions of superlinear elliptic equations and their Morse indices, Commun. Pure Appl. Anal. 45 (1992) 1205-1215, from the Dirichlet boundary condition to the mixed boundary condition. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码：146 / 153
页数：8
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