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

[31] On the Elliptic Problems Involving Multisingular Inverse Square Potentials and Concave-Convex Nonlinearities
Hsu, Tsing-San
ABSTRACT AND APPLIED ANALYSIS, 2011,
[32] EXISTENCE OF SOLUTIONS TO QUASILINEAR ELLIPTIC SYSTEMS WITH COMBINED CRITICAL SOBOLEV-HARDY TERMS
Nyamoradi, Nemat
Javidi, Mohamad
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
[33] The existence of solutions for quasilinear elliptic problems with combined critical Sobolev-Hardy terms
Li, Yuanyuan
Guo, Qianqiao
Niu, Pengcheng
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (01) : 525 - 538
[34] Solutions of Schrodinger equations with inverse square potential and critical nonlinearity
Deng, Yinbin
Jin, Lingyu
Peng, Shuangjie
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (05) : 1376 - 1398
[35] Existence and multiplicity of solutions for a class of p&q elliptic problems with critical exponent
Figueiredo, Giovany M.
MATHEMATISCHE NACHRICHTEN, 2013, 286 (11-12) : 1129 - 1141
[36] EXISTENCE OF SOLUTIONS FOR A SEMILINEAR ELLIPTIC SYSTEM
Benrhouma, Mohamed
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2013, 19 (02) : 574 - 586
[37] SOLUTIONS TO ELLIPTIC SYSTEMS INVOLVING DOUBLY CRITICAL NONLINEARITIES AND HARDY-TYPE POTENTIALS
Kang, Dongsheng
Luo, Jing
Shi, Xiaolin
ACTA MATHEMATICA SCIENTIA, 2015, 35 (02) : 423 - 438
[38] Existence and phase separation of entire solutions to a pure critical competitive elliptic system
Clapp, Monica
Pistoia, Angela
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (01)
[39] Existence of solutions for a class of degenerate quasilinear elliptic equation in RN with vanishing potentials
Bastos, Waldemar D.
Miyagaki, Olimpio H.
Vieira, Ronei S.
BOUNDARY VALUE PROBLEMS, 2013,
[40] Existence and non-existence of solutions for an elliptic system
Covei, Dragos-Patru
APPLIED MATHEMATICS LETTERS, 2014, 37 : 118 - 123

← 1 2 3 4 5 →