Existence of Nodal Solutions for Dirac Equations with Singular Nonlinearities

We prove by a shooting method the existence of infinitely many nodal solutions of the form $\psi(x^0,x) = e^{-i\Omega x^0}\chi(x)$ for nonlinear Dirac equations: \begin{equation*} i\underset{\mu=0}{\overset{3}{\sum}} \gamma^\mu \partial_\mu \psi- m\psi - p|\overline{\psi}\psi|^{p-1}\psi = 0. \end{equation*} with $m>0$, $p\in(0,1)$ and $\chi(x)$ compactly supported under some restrictive conditions over $p$ and the frequency $\Omega>m$. We then study their behavior as $p$ tends to zero to establish the link between theses solutions and the M.I.T. bag model ones.ou