Ground state of a magnetic nonlinear Choquard equation
| Autor: | Gilberto A. Pereira, Hamilton Bueno, Guido G. Mamani |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
[2010]: 35Q55
35Q40 35J20 Applied Mathematics 010102 general mathematics Multiplicity (mathematics) Scalar potential 01 natural sciences 010101 applied mathematics Nonlinear system Mathematics - Analysis of PDEs Simple (abstract algebra) FOS: Mathematics 0101 mathematics Ground state Analysis Mathematical physics Mathematics Vector potential Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1805.06551 |
| Popis: | We consider the stationary magnetic nonlinear Choquard equation \[-(\nabla+iA(x))^2u+ V(x)u=\bigg(\frac{1}{|x|^{\alpha}}*F(|u|)\bigg)\frac{f(|u|)}{|u|}{u},\] where $A: \mathbb{R}^{N}\rightarrow \mathbb{R}^{N}$ is a vector potential, $V$ is a scalar potential, $f\colon\mathbb{R}\to\mathbb{R}$ and $F$ is the primitive of $f$. Under mild hypotheses, we prove the existence of a ground state solution for this problem. We also prove a simple multiplicity result by applying Ljusternik-Schnirelmann methods. Comment: 11 pages |
| Databáze: | OpenAIRE |
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