Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem
KeywordsSchrödinger-Poisson-Slater system, nodal solutions, parabolic problem, dynamical approach
AbstractWe 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.
How to Cite
IANNI, Isabella. Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem. Topological Methods in Nonlinear Analysis [online]. 22 April 2013, T. 41, nr 2, s. 365–385. [accessed 19.10.2021].
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