Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem

By Isabella Ianni. 2011

81 citations recorded by the source corpus.

We consider the Schr\"odinger-Poisson-Slater (SPS) system in $\R^3$ and a nonlocal SPS type equation in balls of $\mathbb R^3$ with Dirichlet boundary conditions. We show that for every $k\in\mathbb N$ each problem considered admits a nodal radially symmetric solution which changes sign exacly $k$ times in the radial variable. Moreover when the domain is the ball of $\mathbb R^3$ we obtain the existence of radial global solutions for the associated nonlocal parabolic problem having $k+1$ nodal regions at every time.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d31c5e97aa9c38b76bb9ea2081841d1d3ee28aeb

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In Applied Mathematics

1. Zhi-Qiang Wang
2. Zhaoli Liu
3. Jianjun Zhang
4. Huan-Song Zhou
5. Wei Shuai
6. Zhengping Wang
7. Qingfang Wang
8. Nikolaos S. Papageorgiou

In Mathematical Physics

1. Zhaoli Liu
2. Zhi-Qiang Wang
3. Jianjun Zhang
4. Huan-Song Zhou
5. Wei Shuai
6. Zhengping Wang
7. Qingfang Wang
8. Thomas Bartsch

Citations in the corpus

• Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$R3 (2015, background): “1), especially on the existence of positive solutions, multiple solutions, sign-changing solutions, ground states and semiclassical states, see for examples, [4,11–15,17,20,21], etc.”
• Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity (2015, unknown): “1 [25] I. Ianni, Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem, Top.”
• Infinitely many sign-changing solutions for the nonlinear Schrödinger–Poisson system (2014, methodology): “Since the approaches in [1,16,20,30], when applied to the monomial nonlinearity f (u) = |u|p−2u, are only valid for p ≥ 4, we want to provide an argument which covers the case p ∈ (3, 4) and this is the second purpose of the present paper.”
• Sign-changing solutions for the nonlinear Schrödinger–Poisson system in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen (2014, methodology): “Based on the LyapunovSchmidt reduction method, in another paper of Ianni and Vaira [12], the existence of nonradially symmetric sign-changing solutions for the semiclassical limit case of (1.1) with V (x) ≡ 1 was established.”