Multiple solutions to the nonlinear Dirac systems on compact spin manifolds with boundary

This paper was concerned with the mutiplicity of solutions to a coupled nonlinear Dirac system on the compact spin manifold with boundary. We set up the variational setting and analysis arguments for the Dirac system accompanied with a potential and the local elliptic boundary condition. More precisely, through the analysis of the spectrum about the Dirac operator with a potential, by the using variational method and truncation technique, we obtained two sequences of solutions with different energies of the system.