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

[1] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[2] Radial solutions of a biharmonic equation with vanishing or singular radial potentials
Badiale, Marino
Greco, Stefano
Rolando, Sergio
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 185 : 97 - 122
[3] SINGULAR QUASILINEAR CRITICAL SCHRODINGER EQUATIONS IN RN
Baldelli, Laura
Filippucci, Roberta
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2022, 21 (08) : 2561 - 2586
[4] Baldelli L, 2022, J GEOM ANAL, V32, DOI 10.1007/s12220-021-00846-3
[5] Bandeira V. P., 2022, LANCET GLOB HEALTH, V64, DOI 10.1016j.nonrwa.2021.103431////
[6] SOLUTION TO BIHARMONIC EQUATION WITH VANISHING POTENTIAL
Bastos, Waldemar D.
Miyagaki, Olimpio H.
Vieira, Ronei S.
[J]. ILLINOIS JOURNAL OF MATHEMATICS, 2013, 57 (03) : 839 - 854
[7] ON SYMMETRICAL SOLUTIONS OF AN ELLIPTIC EQUATION WITH A NONLINEARITY INVOLVING CRITICAL SOBOLEV EXPONENT
BIANCHI, G
CHABROWSKI, J
SZULKIN, A
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 25 (01) : 41 - 59
[8] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
BREZIS, H
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) : 437 - 477
[9] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS
BREZIS, H
LIEB, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) : 486 - 490
[10] Nonlinear critical problems for the biharmonic operator with Hardy potential
D'Ambrosio, Lorenzo
Jannelli, Enrico
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (01) : 365 - 396

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