EXISTENCE AND UNIQUENESS OF SINGULAR SOLUTION TO STATIONARY SCHRoDINGER EQUATION WITH SUPERCRITICAL NONLINEARITY

被引：8
|
作者：
Selem, Fouad Hadj [1 ]
Kikuchi, Hiroaki [2 ]
Wei, Juncheng [2 ]
机构：
[1] Univ Blaise Pascal, CNRS, UMR 6620, Math Lab, F-63171 Aubiere, France
[2] Tsuda Coll, Dept Math, Kodaira, Tokyo 1878577, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 10期
关键词：
Sobolev supercritical; singular solution; harmonic potential; SCALAR FIELD-EQUATIONS; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS;
D O I：
10.3934/dcds.2013.33.4613
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a singular solution to the following elliptic equations: { -Delta mu + vertical bar x vertical bar(2)mu -gimel mu - vertical bar mu vertical bar(p-1)mu = 0, x is an element of R-d, mu(x) > 0, x is an element of R-d, mu (x) -> 0 as vertical bar x vertical bar -> infinity, where d >= 3, gimel > 0 and p > 1. In the spirit of Merle and Peletier [9], we shall show that in case of p > (d + 2)/(d - 2), there is a unique value gimel = gimel(*) such that the equation with gimel = gimel(*) has a unique radial singular solution.
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页码：4613 / 4626
页数：14
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