Existence of Solutions for the Critical Elliptic System with Inverse Square Potentials

被引：1
|
作者：
Liu, Zhao-xia [1 ]
Liu, Zhao-hui [2 ]
机构：
[1] Minzu Univ China, Sch Sci, Dept Informat & Computat Sci, Beijing 100081, Peoples R China
[2] Suncun Middle Sch, Gaoxin Dist Of Jinan 250104, Shandong, Peoples R China
来源：
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2013年 / 29卷 / 02期
基金：
中国国家自然科学基金;
关键词：
elliptic system; variational functional; Palais-Smale condition; critical point; CRITICAL SOBOLEV EXPONENTS; POSITIVE SOLUTIONS; CRITICAL GROWTH; HARDY EXPONENTS; MULTIPLE SOLUTIONS; EQUATIONS; INEQUALITIES;
D O I：
10.1007/s10255-013-0225-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let Omega there exists 0 be an open bounded domain in R-N (N >= 3) and 2*(s) = 2(N-s)/N-2, 0 < s < 2. We consider the following elliptic system of two equations in H-0(1)(Omega) x H-0(1)(Omega): -Delta u-tu/vertical bar x vertical bar(2) = 2 alpha/alpha+beta vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta)/vertical bar x vertical bar(3) + lambda v, -Delta u-tv/vertical bar x vertical bar(2) = 2 beta/alpha+beta vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2)v/vertical bar x vertical bar(3) + mu v, where lambda, mu > 0 and alpha, beta > 1 satisfy alpha + beta = 2*( s). Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain- Pass theorem, we establish the existence of solutions.
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页码：315 / 328
页数：14
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