An existence result for Schrödinger equations with magnetic fields and exponential critical growth
| Autor: | Giovany M. Figueiredo, Sara Barile |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Numerical Analysis Theoretical and experimental justification for the Schrödinger equation Partial differential equation Applied Mathematics 010102 general mathematics Mathematics::Analysis of PDEs 01 natural sciences Schrödinger field Exponential function Schrödinger equation Magnetic field 010101 applied mathematics symbols.namesake symbols Magnetic potential Nabla symbol 0101 mathematics Analysis Mathematical physics Mathematics |
| Zdroj: | Journal of Elliptic and Parabolic Equations. 3:105-125 |
| ISSN: | 2296-9039 2296-9020 |
| DOI: | 10.1007/s41808-017-0007-9 |
| Popis: | We show the existence of a complex solution to the following magnetic Schrodinger equation $$\begin{aligned} - (\nabla + i A(x) )^2 \, u + u = f(|u|^2) u \quad \hbox {in} \, \mathbb R^2 \end{aligned}$$ where $$A: \mathbb R^2 \rightarrow \mathbb R^2$$ 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., $$A(x) = 0$$ ). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink