文献类型：期刊文献

英文题名：CONCENTRATION PHENOMENA FOR NONLINEAR MAGNETIC SCHRODINGER EQUATIONS WITH CRITICAL GROWTH

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

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

年份：2021

卷号：241

期号：1

起止页码：465

外文期刊名：ISRAEL JOURNAL OF MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000618607300009)】；

基金：C. Ji is partially supported by Natural Science Foundation of Shanghai (20ZR1413900, 18ZR1409100). The authors would like to thank the referee for several useful comments.

语种：英文

摘要：In this paper, we are concerned with the following nonlinear magnetic Schrodinger equation with critical growth: {(epsilon/i del - A(x))(2)u+V(x)u = f(vertical bar u vertical bar(2))u + vertical bar u vertical bar(2)*(-2) in R-N, u is an element of H-1(R-N, C), where epsilon > 0 parameter, N >= 3 and 2* = 2N/N-2 is the Sobolev critical exponent, V: R-N -> R and A: R-N -> R-N are continuous potentials, f: R -> R is a subcritical nonlinear term. Under a local assumption on the potential V, by the variational methods, the penalization technique and the Ljusternic-Schnirelmann theory, we prove the multiplicity and concentration of nontrivial solutions of the above problem for epsilon small. For the problem, the function f is only continuous, which allows to consider larger classes of nonlinearities in the reaction.