We consider the Schroedinger–Poisson–Slater (SPS) system in R3 and a nonlocal SPS type equation in balls of R3 with Dirichlet boundary conditions. We show that for every k ∈ 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 R3 we obtain the existence of radial global solutions for the associated nonlocal parabolic problem having k + 1 nodal regions at every time.
Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem / Ianni, I. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 41:(2013), pp. 365-385.
Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem
IANNI I
2013
Abstract
We consider the Schroedinger–Poisson–Slater (SPS) system in R3 and a nonlocal SPS type equation in balls of R3 with Dirichlet boundary conditions. We show that for every k ∈ 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 R3 we obtain the existence of radial global solutions for the associated nonlocal parabolic problem having k + 1 nodal regions at every time.| File | Dimensione | Formato | |
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