The fibering method approach for a non-linear schrodinger equation coupled with the electromagnetic field
| Autor: | Gaetano Siciliano, Kaye Silva |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Electromagnetic field
35J91 Nehari manifold General Mathematics variational methods Characterization (mathematics) 35J50 01 natural sciences Schrödinger equation symbols.namesake Mathematics - Analysis of PDEs Variational methods 35Q60 FOS: Mathematics 0101 mathematics Fibering methods 35A02 35J50 35J91 35Q60 Mathematics EQUAÇÕES DIFERENCIAIS PARCIAIS 010102 general mathematics Mathematical analysis Schrödinger-poisson type system 35A02 Nonlinear system Schrödinger-Poisson type system fibering methods symbols Energy (signal processing) Analysis of PDEs (math.AP) |
| Zdroj: | Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) Recercat. Dipósit de la Recerca de Catalunya instname Publ. Mat. 64, no. 2 (2020), 373-390 Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona |
| Popis: | We study, with respect to the parameter $q\neq0$, the following Schr\"odinger-Bopp-Podolsky system in $\mathbb R^{3}$ \begin{equation*} \left\{ \begin{aligned} -&\Delta u+\omega u+q^2\phi u=|u|^{p-2}u, \\ &-\Delta \phi+a^2\Delta^2 \phi = 4\pi u^2, \end{aligned} \right. \end{equation*} where $p\in(2,3], \omega>0, a\geq0$ are fixed. We prove, by means of the fibering approach, that the system has no solutions at all for large values of $q's$, and has two radial solutions for small $q's$. We give also qualitative properties about the energy level of the solutions and a variational characterization of these extremals values of $q$. Our results recover and improve some results in the literature. |
| Databáze: | OpenAIRE |
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