On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials

By Isabella Ianni, Giusi Vaira. 2008

152 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/262c2ad12556326300d5d5f82a1f036c11df0218

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains (2013, background): “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].”
Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem (2011, background): “1) shows several difficulties, the nonlinear 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 [1], [2], [4], [9]–[12], [16], [19]–[21], [26], see also [”
Infinitely many sign-changing solutions for the nonlinear Schrödinger–Poisson system (2014, background): “Here, we would also like to mention the papers [4,14,15,17,21,29] for related topics.”
The concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system (2017, unknown): “In [23], Ianni and Vaira considered the following system ⎧ ⎨ ⎩ −ε2 u + V (x)u + φu = f (u), in R3, − φ = u2, in R3.”
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): “(i i) We treat more general nonlinearity f than in [20,27,3,2,17,28,21].”
On Schrödinger-Poisson Systems (2008, background): “The existence of spike-like solutions will be discussed, following the recent paper [ 11 ].”
Multiplicity and concentration of positive solutions for the fractional Schrödinger–Poisson systems with critical growth (2017, unknown): “For more results on the semiclassical states we refer the readers to [3,27,30,33,48] and the references therein.”