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High perturbations of Choquard equations with critical reaction and variable growth
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-06-04 , DOI: 10.1090/proc/15469
Youpei Zhang , Xianhua Tang , Vicenţiu D. Rădulescu

Abstract: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.


中文翻译:

具有临界反应和可变增长的 Choquard 方程的高扰动

摘要:本文涉及一类新的Choquard方程解的数学分析。本文所研究问题的主要特点如下:(i)方程由一个变指数微分算子驱动;(ii) Choquard 术语包含具有双变量增长的非标准潜力;(iii) 反应缺乏紧凑性,这是由临界非线性产生的。主要结果确定了在源项高度扰动的情况下存在无限多个解。该证明结合了变分方法和解析方法,包括变量指数的 Hardy-Littlewood-Sobolev 不等式和变量增长问题的集中紧凑性原理。
更新日期:2021-07-27
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