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 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.