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

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 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.

Cited by in corpus (1)

• Existence of positive multi-bump solutions for a Schrödinger-Poisson system in ${\mathbb{R}}^3$