HIGH PERTURBATIONS OF CHOQUARD EQUATIONS WITH CRITICAL REACTION AND VARIABLE GROWTH

被引：4

作者：

Zhang, Youpei ^{[1
,2
]}

Tang, Xianhua ^{[1
]}

Radulescu, Vicentiu D. ^{[2
,3
,4
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Univ Craiova, Dept Math, Craiova 200585, Romania

[3] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[4] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, Bucharest 014700, Romania

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Choquard equation; anisotropic Sobolev space; Hardy-Littlewood-Sobolev inequality; concentration-compactness principle; EXISTENCE;

D O I：

10.1090/proc/15469

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the mathematical analysis of solutions for a new class of Choquard equations. The main features of the problem studied in this paper are the following: (i) the equation is driven by a differential operator with variable exponent; (ii) the Choquard term contains a nonstandard potential with double variable growth; and (iii) the lack of compactness of the reaction, which is generated by a critical nonlinearity. The main result establishes the existence of infinitely many solutions in the case of high perturbations of the source term. The proof combines variational and analytic methods, including the Hardy-Littlewood-Sobolev inequality for variable exponents and the concentration-compactness principle for problems with variable growth.

引用

页码：3819 / 3835

页数：17

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