Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit

In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices. Precisely, we discuss existence and multiplicity of the bound states (arising as critical points of the NLD action functional) and we prove that, in the L^2 -subcritical case, they converge to the bound states of the nonlinear Schr"odinger equation in the nonrelativistic limit.