Eigenvalue Curves for Generalized MIT Bag Models

We study spectral properties of Dirac operators on bounded domains $$\Omega \subset {\mathbb {R}}^3$$ with boundary conditions electrostatic and Lorentz scalar type which depend a parameter $$\tau \in \mathbb {R}$$ ; the case = 0$$ corresponds to MIT bag model. show that eigenvalues are parametrized as increasing functions $$ , we exploit this monotonicity limits \rightarrow \pm \infty . prove if is not ball then first positive eigenvalue greater than one same volume for all large enough. Moreover, converges mass particle \downarrow -\infty also analyze its order asymptotics.