On the existence of solutions for the Schrödinger-Poisson equations

By Leiga Zhao, Fukun Zhao. 2008

336 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9088a51f5966adf1bfe01a7f5c0db6d82b7bccdb

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Existence of positive solutions to Schrödinger–Poisson type systems with critical exponent (2014, result): “Related results for more general f were also obtained in [1, 28, 32], and solutions of Schrödinger–Poisson systems with nonconstant potential (where b is a function of x) were considered in [17, 20, 21, 30, 31].”
The concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system (2017, neutral): “See [1,25,36,44,48] and the references therein for the existence of solutions.”
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): “Proof As in [14,35], one can easily check the conclusions (i) and (i i).”
On ground state solutions for some non-autonomous Schrödinger–Poisson systems☆ (2012, methodology): “In recent years, system (SP) has been studied widely via modern variational methods under the various hypotheses, see [1,3,5,6,19,26] and the references therein.”
Positive solutions of an asymptotically periodic Schrödinger–Poisson system with critical exponent☆ (2016, background): “1) was studied in [13] and existence of infinitely many geometrically distinct solutions was proved by a superposition principle established in [14].”
Infinitely many sign-changing solutions for the nonlinear Schrödinger–Poisson system (2014, background): “This assumptionwas introduced in [31,32] in order to prove compactnesswith themonotonicity trick of Jeanjean [19].”
Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in $R^3$ (2013, methodology): “1 can be viewed as a partial extension of a main result in [16] and extends the main result in [36] to the Kirchhoff equation.”
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 (SP )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, 35-37] and the references therein.”
Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials (2017, background): “In [34], the authors proved that the following nonlinear Schrödinger-Poission problem { −4u+ V (x)u+ φu = |u|p−2u, x ∈ R(3), −4φ = u(2), x ∈ R(3) (1.”
On the Schrödinger-Maxwell equations under the effect of a general nonlinear term (2009, background): “The greatest part of the literature focuses on the study of the previous system for the very special nonlinearity g(u) = −u + |u|u, and existence, nonexistence and multiplicity results are provided in many papers for this particular problem (see [1, 2, 10, 12, 13, 14, 19, 20, 21, 24, 28]).”