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2013 Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem
Isabella Ianni
Topol. Methods Nonlinear Anal. 41(2): 365-385 (2013).

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.

Citation

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Isabella Ianni. "Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem." Topol. Methods Nonlinear Anal. 41 (2) 365 - 385, 2013.

Information

Published: 2013
First available in Project Euclid: 21 April 2016

zbMATH: 1330.35128
MathSciNet: MR3114313

Rights: Copyright © 2013 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.41 • No. 2 • 2013
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