文献类型：期刊文献

英文题名：Multi-bump solutions for the nonlinear magnetic Schrodinger equation with exponential critical growth in R2

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

机构：[1]East China Univ Sci & Technol, Dept 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]King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

年份：2021

卷号：164

期号：3-4

起止页码：509

外文期刊名：MANUSCRIPTA MATHEMATICA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000522567200001)】；

基金：C. Ji was supported by Shanghai Natural Science Foundation (18ZR1409100).

语种：英文

外文关键词：Nonlinear Schrodinger equation; Magnetic field; Exponential critical nonlinearity; Multi-bump solution; Variational methods

摘要：In this paper, using variational methods, we establish the existence and multiplicity of multi-bump solutions for the following nonlinear magnetic Schrodinger equation -( backward difference +iA(x))2u+(lambda V(x)+Z(x))u=f(|u|2)uinR2, where lambda>0 , f(t) is a continuous function with exponential critical growth, the magnetic potential A:R2 -> R2 and the potentials V, Z:R2 -> R are continuous functions verifying some natural conditions. We show that if the zero set of the potential V has several isolated connected components omega 1, horizontal ellipsis ,omega ksuch that the interior of omega j is non-empty and partial differential omega j is smooth, then for lambda>0 large enough, the equation has at least 2k-1 multi-bump solutions.