Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities

被引：9
|
作者：
Selem, Fouad Hadj [1 ]
Kikuchi, Hiroaki [2 ]
机构：
[1] Univ Reims, Math Lab, F-51687 Reims 02, France
[2] Hokkaido Univ, Dept Math, Kita Ku, Sapporo, Hokkaido 0600810, Japan
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 387卷 / 02期
基金：
日本学术振兴会;
关键词：
Sobolev critical exponent; Sobolev supercritical exponent; Bifurcation branch; SCALAR FIELD-EQUATIONS; POSITIVE SOLUTIONS; BALL;
D O I：
10.1016/j.jmaa.2011.09.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence and non-existence of the positive solution to a semilinear elliptic equation with the harmonic potential and power type nonlinearity. First, we obtain non-existence result in three space dimension with the Sobolev critical nonlinearity. Next, we prove that there exists a global bifurcation branch with the Sobolev supercritical nonlinearity. (C) 2011 Elsevier Inc. All rights reserved.
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页码：746 / 754
页数：9
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