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.

引用

页码：315 / 328

页数：14

共 50 条

[41] Infinitely Many Solutions for a Critical Elliptic System with Hardy Potentials and Concave Nonlinearities
Echarghaoui, Rachid
Hatimi, Abdelouhab
Zaimi, Zakaria
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2024, 21 (08)
[42] Symmetric solutions for a class of singular biharmonic elliptic systems involving critical exponents
Deng, Zhiying
Huang, Yisheng
APPLIED MATHEMATICS AND COMPUTATION, 2015, 264 : 323 - 334
[43] Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent
Xiu, Zonghu
ABSTRACT AND APPLIED ANALYSIS, 2012,
[44] Infinitely many solutions to elliptic systems with critical exponents and Hardy potentials
Wang, Li
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (12) : 1558 - 1568
[45] Existence of sign-changing solutions for semilinear singular elliptic equations with critical Sobolev exponents
Guo, Qianqiao
Niu, Pengcheng
Cui, Xuewei
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 361 (02) : 543 - 557
[46] Infinitely many solutions to elliptic systems with critical exponents and Hardy potentials
Kang DongSheng
Peng ShuangJie
SCIENCE CHINA-MATHEMATICS, 2012, 55 (10) : 2027 - 2044
[47] Boundary singularities of solutions of semilinear elliptic equations with critical Hardy potentials
Gkikas, Konstantinos T.
Veron, Laurent
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 : 469 - 540
[48] Existence of solutions for singular critical semilinear elliptic equation
Wang, Mengchao
Zhang, Qi
APPLIED MATHEMATICS LETTERS, 2019, 94 : 217 - 223
[49] Infinitely many solutions for elliptic systems with critical exponents
Liu, Zhaoxia
Han, Pigong
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 353 (02) : 544 - 552
[50] Existence of infinitely many solutions for critical sub-elliptic systems via genus theory
Jiao, Hongying
Zhu, Shuhai
Zhang, Jinguo
COMMUNICATIONS IN ANALYSIS AND MECHANICS, 2024, 16 (02): : 237 - 261

← 1 2 3 4 5 →