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

Author(s)

D'Avenia, Pietro ^[1] ; Siciliano, Gaetano ^[2]

Affiliation

^[1] Politecn Bari, Dipartimento Meccan Matemat & Management, Via Orabona 4, I-70125 Bari - Italy

^[2] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 267, n. 2, p. 1025-1065, JUL 5 2019.
• Web of Science Citations: 1

Abstract

We study the following nonlinear Schrodinger-Bopp-Podolsky system [-Delta u + omega u + q(2) phi u = vertical bar u vertical bar(p-2)u in R-3 -Delta phi + a(2)Delta(2)phi = 4 pi u(2) with a, omega > 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 Schrodinger Poisson system as a -> 0. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/17264-4 - Existence of solutions for nonlinear elliptic equations
• Grantee: Gaetano Siciliano
• Support Opportunities: Regular Research Grants