Linear and nonlinear eigenvalue problems for Dirac systems in unbounded domains

TL;DR

This paper investigates eigenvalue problems for Dirac systems in unbounded domains, analyzing linear and nonlinear cases, and establishing bifurcation results and solution properties.

Contribution

It introduces new bifurcation results and solution characterizations for nonlinear Dirac systems in unbounded domains.

Findings

Describes nodal properties of solutions via rotation number

Establishes a global bifurcation result for nonlinear Dirac systems

Provides a continuum of solutions with specific forms

Abstract

We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear Dirac system in the open half-line. As an application, we provide a global continuum of solutions of the nonlinear Dirac equation which have a special form.