数学
索波列夫空间
变量(数学)
紧凑空间
数学分析
非线性系统
操作员(生物学)
期限(时间)
微分方程
临界变量
应用数学
物理
统计物理学
量子力学
化学
抑制因子
基因
转录因子
生物化学
伊辛模型
作者
Youpei Zhang,Xianhua Tang,Vicenţiu D. Rădulescu
出处
期刊:Proceedings of the American Mathematical Society
[American Mathematical Society]
日期:2021-06-04
卷期号:149 (9): 3819-3835
被引量:2
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.
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