Topological Methods in Nonlinear Analysis

Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem

Isabella Ianni

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Abstract

We consider the Schrödinger-Poisson-Slater (SPS) system in $\mathbb R^3$ 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 exactly $k$ 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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 41, Number 2 (2013), 365-385.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461245483

Mathematical Reviews number (MathSciNet)
MR3114313

Zentralblatt MATH identifier
1330.35128

Citation

Ianni, Isabella. Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem. Topol. Methods Nonlinear Anal. 41 (2013), no. 2, 365--385. https://projecteuclid.org/euclid.tmna/1461245483


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