Nonrelativistic limit of solitary waves for nonlinear Maxwell–Klein–Gordon equations

We study the nonrelativistic limit of solitary waves from Nonlinear Maxwell–Klein–Gordon equations (NMKG) to Nonlinear Schrödinger–Poisson equations (NSP). It is known that the existence or multiplicity of positive solutions depends on the choices of parameters the equations contain. In this paper, we prove that for a given positive solitary wave of NSP, which is found in Ruiz’s work (J Funct Anal 237(2):655–674, 2006), there corresponds a family of positive solitary waves of NMKG under the nonrelativistic limit. Notably, our results contain a new result of existence of positive solutions to (NMKG) with lower order nonlinearity.