Multiplicity and Nonrelativistic limit of Bound States of Nonlinear Dirac Equations on Noncompact Metric Graphs with Localized Nonlinearities

Abstract

In this paper, we investigate the multiplicity of normalized solutions to a nonlinear Dirac equation with localized nonlinearities on noncompact metric graphs under the \(L^2\)-constraint, as well as the asymptotic behavior of these solutions in the nonrelativistic limit. First, we establish the existence of multiple normalized bound states. Moreover, we explore the nonrelativistic limit and show that, as the speed of light tends to infinity, the solutions converge to those of a nonlinear Schrödinger equation. Our results including the mass-subcritical, mass-critical and, in particular, mass-supercritical regimes.