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 / D'Avenia, Pietro; Siciliano, Gaetano. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 267:2(2019), pp. 1025-1065. [10.1016/j.jde.2019.02.001]

Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: Solutions in the electrostatic case

Pietro d'Avenia
;
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→0
2019
Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: Solutions in the electrostatic case / D'Avenia, Pietro; Siciliano, Gaetano. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 267:2(2019), pp. 1025-1065. [10.1016/j.jde.2019.02.001]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/163475
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