Nonlinear Schr\"odinger equation with bounded magnetic field
Giuseppe Devillanova, Cyril Tintarev
TL;DR
This paper investigates the existence of solutions to the nonlinear Schrödinger equation influenced by a bounded magnetic field, without requiring periodicity or electric fields, using advanced functional analysis techniques.
Contribution
It introduces a general structural approach for bounded sequences in magnetic Sobolev spaces to establish solution existence without lattice periodicity or electric fields.
Findings
Existence of solutions established for nonlinear Schrödinger equations with bounded magnetic fields.
No assumptions of lattice periodicity or external electric fields are needed.
A new structural result for bounded sequences in magnetic Sobolev spaces is developed.
Abstract
The paper studies existence of solutions for the nonlinear Schr\"odinger equation with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic Sobolev space.
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