Existence and multiplicity results for a singular fourth-order elliptic system involving critical homogeneous nonlinearities

被引：0

作者：

Deng, Zhiying ^{[1
]}

Huang, Yisheng ^{[2
]}

机构：

[1] Chongqing Univ Posts & Telecommun, Sch Sci, Chongqing 400065, Peoples R China

[2] Soochow Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 04期

关键词：

Hardy-Rellich inequality; group invariant solution; variational methods; fourth-order elliptic system; BIHARMONIC EQUATION; SCHRODINGER-EQUATIONS; OPERATOR;

D O I：

10.3934/math.2023453

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with a singular fourth-order elliptic system involving critical homogeneous nonlinearities. The existence and multiplicity results of group invariant solutions are established by variational methods and the Hardy-Rellich inequality.

引用

页码：9054 / 9073

页数：20

共 34 条

[11] de Morais DC, 1999, COMMUN PART DIFF EQ, V24, P1537
[12] Multiple symmetric results for singular quasilinear elliptic systems with critical homogeneous nonlinearity
Deng, Zhiying
Zhang, Rui
Huang, Yisheng
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (05) : 1538 - 1552
[13] Symmetric solutions for a class of singular biharmonic elliptic systems involving critical exponents
Deng, Zhiying
Huang, Yisheng
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 264 : 323 - 334
[14] Ground state solution to the biharmonic equation
Feng, Zhaosheng
Su, Yu
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (01):
[15] On multiplicity and concentration behavior of solutions for a critical system with equations in divergence form
Figueiredo, Giovany M.
Salirrosas, Segundo Manuel A.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 494 (01)
[16] EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR KIRCHHOFF SYSTEM WITH CRITICAL GROWTH
Furtado, Marcelo F.
de Oliveira, Luan D.
da Silva, Joao Pablo P.
[J]. ANNALES FENNICI MATHEMATICI, 2021, 46 (01): : 295 - 308
[17] Multiplicity of solutions for homogeneous elliptic systems with critical growth
Furtado, Marcelo F.
da Silva, Joao Pablo P.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (02) : 770 - 785
[18] BIHARMONIC SYSTEMS INVOLVING MULTIPLE RELLICH TYPE POTENTIALS AND CRITICAL RELLICH SOBOLEV NONLINEARITIES
Kang, Dongsheng
Xu, Liangshun
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (02) : 333 - 346
[19] Existence and nonexistence results for critical biharmonic systems involving multiple singularities
Kang, Dongsheng
Xiong, Ping
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 452 (01) : 469 - 487
[20] Ground state solutions to biharmonic equations involving critical nonlinearities and multiple singular potentials
Kang, Dongsheng
Xiong, Ping
[J]. APPLIED MATHEMATICS LETTERS, 2017, 66 : 9 - 15

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