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

Authors
  • Ianni, Isabella
Type
Published Article
Publication Date
Aug 13, 2011
Submission Date
Aug 13, 2011
Identifiers
arXiv ID: 1108.2803
Source
arXiv
License
Yellow
External links

Abstract

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.

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