We study the following nonlinear Schrödinger–Bopp–Podolsky system {−Δu+ωu+q 2 ϕu=|u| p−2 u−Δϕ+a 2 Δ 2 ϕ=4πu 2 inR 3 with a,ω>0. We prove existence and nonexistence results depending on the parameters q,p. Moreover we also show that, in the radial case, the solutions we find tend to solutions of the classical Schrödinger–Poisson system as a→0
Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: Solutions in the electrostatic case
Pietro d'Avenia
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2019-01-01
Abstract
We study the following nonlinear Schrödinger–Bopp–Podolsky system {−Δu+ωu+q 2 ϕu=|u| p−2 u−Δϕ+a 2 Δ 2 ϕ=4πu 2 inR 3 with a,ω>0. We prove existence and nonexistence results depending on the parameters q,p. Moreover we also show that, in the radial case, the solutions we find tend to solutions of the classical Schrödinger–Poisson system as a→0File in questo prodotto:
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