文献类型：期刊文献

英文题名：Multi-bump solutions for the nonlinear magnetic Choquard equation with deepening potential well

作者：Ji, Chao[1];Radulescu, Vicentiu D.[2,3,4]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland;[3]Univ Craiova, Dept Math, Craiova 200585, Romania;[4]Romanian Acad, Simion Stoilow Inst Math, POB 1-764, Bucharest 014700, Romania

年份：2022

卷号：306

起止页码：251

外文期刊名：JOURNAL OF DIFFERENTIAL EQUATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000714680000008)】；

基金：C. Ji was partially supported by National Natural Science Foundation of China (No. 12171152) and Natural Science Foundation of Shanghai (No. 20ZR1413900). The research of Vicentiu D. R.adulescu was supported by a grant of the Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI, project number PCE 137/2021, within PNCDI III.

语种：英文

外文关键词：Nonlinear Choquard equation; Magnetic field; Multi-bump solution; Variational methods

摘要：In this paper, using variational methods, we study multiplicity of multi-bump solutions for the following nonlinear magnetic Choquard equation {-(del+iA(x))(2)u+(lambda V(x) +1)u =(1/vertical bar x vertical bar(mu) * vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u x is an element of R-N, u is an element of H-1(R-N, C) where N >= 2, lambda > 0 is a real parameter, 0 < mu < 2, i is the imaginary unit, p is an element of (2, 2*(2(N-mu)/2N)), where 2* = 2N/N-2 if N >= 3, 2* +infinity, if N = 2. The magnetic potential A is an element of L-loc(2) (R-N , R-N) and V : R-N -> R is a nonnegative continuous function. We show that if the zero set of V has several isolated connected components Omega(1), ..., Omega(k) such that the interior of Omega(j) is non-empty and partial derivative Omega(j) is smooth, then for h > 0 large enough, the above equation has at least 2(k) - 1 multi-bump solutions. (C) 2021 Elsevier Inc. All rights reserved.