Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations

By Teresa D'Aprile, Dimitri Mugnai. Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2004

518 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0c7f53299e946aa62c68d81bc53eedb631e3ecb7

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Citations in the corpus

Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem (2011, methodology): “ear nature of it being due both to the power-type nonlinearity in the ﬁrst equation and to the coupling, and has been object of many investigation in the last years (we recall among others the papers [3, 4, 5, 10, 12, 13, 14, 20, 24], see also [19]). As shown by recent results the structure of the s”
The Schrödinger–Poisson equation under the effect of a nonlinear local term (2006, background): “In [12] the (PS) condition is proved only for p ∈ [3,5), and then their existence result is restricted to that case.”
Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains (2013, methodology): “case where Ω = R , see the papers of Azzollini & Pomponio [5], Cerami & Vaira [13], Coclite [14], D’Aprile & Mugnai [15, 16], d’Avenia [17], Ianni [20], Kikuchi [19], and Zhao & Zhao [29].”
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, unknown): “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]).”
Multiple bound states for the Schroedinger-Poisson problem (2008, background): “is of class C1 and its critical points are classical solutions of (2), see, for instance, [3, 6].”
On ground state solutions for some non-autonomous Schrödinger–Poisson systems☆ (2012, background): “Third, it is not difficult to find that every (PS) sequence is bounded when 3 < p < 5 in [10] because a variant of global Ambrosetti–Rabinowitz condition is satisfied when 3 < p < 5 (see [11]).”
Standing waves of nonlinear Schrödinger equations with the gauge field (2012, result): “7) can be compared to recent interesting studies (see [1,3,6,12] and references therein) on the Schrödinger–Poisson equation u − ωu − μ ( 1 |x| ∗ |u| 2 ) u + |u|q−2u = 0 in R3, (1.”
Schrodinger-Poisson system with steep potential well (2009, background): “4 of [10] showed that u and φu (simply by φ, sometimes) satisfy (1.”