Non-Existence Results for the Coupled Klein-Gordon-Maxwell Equations

By Teresa D'Aprile, Dimitri Mugnai. 2004

383 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9b3462989dee6fa7605c5e577e5cdffc36e82b99

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Citations in the corpus

Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials (2017, background): “Furthermore, in [13] a related Pohozaev equality is found.”
Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem (2011, background): “1) doesn’t admit any nontrivial solution (see [11], [21], [26]), while when q ∈ (2, 5) existence and multiplicity results have been proved using variational techniques.”
Existence and concentration of positive solutions for semilinear Schrödinger–Poisson systems in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} (2012, neutral): “These theories consist of field equations that provide a model to describe the interaction of a nonlinear Schrödinger field with the electromagnetic field (see [26,15,16]).”
Ground state solutions for the nonlinear Schrödinger–Maxwell equations (2007, background): “It can be proved (see [14, 20]) that if (u, φ) ∈ H(1)(R(3))×D(1,2)(R(3)) is a solution of (1), then it satisfies the following Pohozaev type identity ∫”
Multiple bound states for the Schroedinger-Poisson problem (2008, background): “The solutions of (12) must also verify a Pohozaev equality, as was proved in [7] (see equation (4.”
The Schrödinger–Poisson equation under the effect of a nonlinear local term (2006, methodology): “Keywords: Schrödinger–Poisson equation; Variational methods; Pohozaev equality; Lagrange multiplier rule”
Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential (2015, background): “There has been a vast literature on the study of existence and multiplicity of solutions of system (S P)λ under various hypotheses on the potential V (x) and the nonlinearity f (x, u), see [1–3,5,9–14,18,19,21,22,24–28,31,34–37] and the references therein.”