Multiple high energy solutions of a nonlinear Hardy-Sobolev critical elliptic equation arising in astrophysics

被引：0

作者：

Mao, Suzhen ^{[1
]}

Xia, Aliang ^{[2
,3
]}

Xu, Yan ^{[2
]}

机构：

[1] Nanchang Inst Technol, Sch Sci, Nanchang 330099, Jiangxi, Peoples R China

[2] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China

[3] Jiangxi Normal Univ, Jiangxi Prov Ctr Appl Math, Nanchang 330022, Jiangxi, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 247卷

关键词：

Variational methods; Lack of compactness; High energy solutions; POSITIVE SOLUTIONS; INEQUALITY; EXISTENCE;

D O I：

10.1016/j.na.2024.113602

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the existence and multiplicity of high energy solutions to the problem proposed as a model for the dynamics of galaxies: -Delta u + V(x)u = |u|(2)(-2)(*) u/|y|, x = (y, z) is an element of R-n x Rn-n, where n > 4, 2 m <n, 2(*) := 2(n-1)/n-2 and potential function V(x) : R-n -> R. Benefiting from a global compactness result, we show that there exist at least two positive high energy solutions. Our proofs are based on barycenter function, quantitative deformation lemma and Brouwer degree theory.

引用

页数：15

共 22 条

[1] Positive solutions to a semilinear elliptic equation with a Sobolev-Hardy term [J].

Al-aati, Ali ;

Wang, Chunhua ;

Zhao, Jing .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (14) :4847-4861

[2] Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian [J].

Alves, CO .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (07) :1187-1206

[3] A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics [J].

Badiale, M ;

Tarantello, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 163 (04) :259-293

[4] EXISTENCE OF POSITIVE SOLUTIONS OF THE EQUATION -DELTA-U+A(X)U=U(N+2)/(N-2) IN RN [J].

BENCI, V ;

CERAMI, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 88 (01) :90-117

[5]

BERTIN G, 2000, DYNAMICS GALAXIES

[6] Multiple positive bound states for critical Schrodinger-Poisson systems [J].

Cerami, Giovanna ;

Molle, Riccardo .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25

[7]

Chen X., 2013, Electron. J. Differential Equations, P12

[8]

Ciotti L., 2001, Dynamical models in astrophysics

[9]

Correia JN, 2019, CALC VAR PARTIAL DIF, V58, DOI 10.1007/s00526-019-1502-7

[10] High energy positive solutions for a coupled Hartree system with Hardy-Littlewood-Sobolev critical exponents [J].

Gao, Fashun ;

Liu, Haidong ;

Moroz, Vitaly ;

Yang, Minbo .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 287 :329-375

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