An existence result for Schrödinger equations with magnetic fields and exponential critical growth

被引：10
作者：
Barile S. [1 ]
Figueiredo G.M. [2 ]
机构：
[1] Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via E. Orabona 4, Bari
[2] Universidade de Brasilia-UNB Departamento de Matemática, Campus Universitário Darcy Ribeiro, Brasilia, CEP 70.910-900, DF
来源：
Journal of Elliptic and Parabolic Equations | 2017年 / 3卷 / 1-2期
关键词：
Compactness lemma; Magnetic Schrödinger equations; Critical exponential nonlinearity; Minimization problem; Trudinger-Moser inequality;
D O I：
10.1007/s41808-017-0007-9
中图分类号：
学科分类号：
摘要：
We show the existence of a complex solution to the following magnetic Schrödinger equation -(∇+iA(x))2u+u=f(|u|2)uinR2where A: R2→ R2 is a suitable magnetic potential and f satisfies exponential critical growth assumptions at infinity. We exploit some recent results established by means of a Trudinger-Moser inequality to the corresponding real equation in absence of the magnetic field (i.e., A(x) = 0). © 2017, Orthogonal Publishing and Springer International Publishing AG, part of Springer Nature.
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页码：105 / 125
页数：20
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