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.

引用

页码：105 / 125

页数：20

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