Multiplicity and asymptotics of steady-state solutions to the Dirac–Bopp–Podolsky system

This paper investigates the following Dirac–Bopp–Podolsky system: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are [Formula: see text] Pauli–Dirac matrices. Under some suitable conditions for the external potential [Formula: see text] and the nonlinearity [Formula: see text], we establish the existence and multiplicity of steady-state solutions by using variational method and nonlocal analysis techniques. Moreover, we regard [Formula: see text] as a parameter and study the asymptotic behaviors of solutions as [Formula: see text], which reflect some relationship between [Formula: see text] and [Formula: see text].