### 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.

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.

#### Keywords

Schrödinger-Poisson-Slater system; nodal solutions; parabolic problem; dynamical approach

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