Electro-magneto-static study of the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca setting

Abstract

We investigate the system consisting of the the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca setting in the context of closed 3-dimensional manifolds. We prove existence of solutions up to the gauge, and compactness of the system both in the subcritical and in the critical case.2010 Mathematics Subject Classification. 35G50, 58J99.

Multiple solutions for a Schrödinger–Bopp–Podolsky system with positive potentials

“…Actually there are few papers on Schrödinger-Bopp-Podolsky systems. We cite also [9,17] where the authors study the critical case, [16] where the problem has been studied in the Proca setting on 3 closed manifolds, and [21] where the fibering method of Pohozaev has been used to deduce existence of solutions (depending on a parameter) and even nonexistence.…”

Existence and asymptotic behavior of solutions to eigenvalue problems for Schrodinger-Bopp-Podolsky equations

“…In particular the problem has been addressed in the whole space and in bounded domains, where existence and multiplicity of solutions have been proved by using variational methods and critical point theory. We refer the reader to the recent papers [2,5,7,9,10,11,13].…”

Multiple solutions and profile description for a nonlinear Schrödinger-Bopp-Podolsky-Proca system on a manifold

“…In the last few years a wide literature on this topic is developing both in R 3 (see [7,8,11,12,[21][22][23]26,27] and references therein) and on manifolds, due to Hebey (see [16][17][18][19]).…”