Multiplicity and concentration of semi-classical solutions to nonlinear Dirac-Klein-Gordon systems

Abstract

In the present article, we study multiplicity of semi-classical solutions of a Yukawa-coupled massive Dirac-Klein-Gordon system with the general nonlinear self-coupling, which is either subcritical or critical growth. The number of solutions obtained is described by the ratio of maximum and behavior at infinity of the potentials. We use the variational method that relies upon a delicate cutting off technique. It allows us to overcome the lack of convexity of the nonlinearities.