1208.2453 (Loïc Le Treust)

Existence of nodal solutions for Dirac equations with singular
nonlinearities    [PDF]

Loïc Le Treust

We prove, by a shooting method, the existence of infinitely many solutions of the form $\psi(x^0,x) = e^{-i\Omega x^0}\chi(x)$ of the nonlinear Dirac equation i\underset{\mu=0}{\overset{3}{\sum}} \gamma^\mu \partial_\mu \psi- m\psi - F(\bar{\psi}\psi)\psi = 0 where $\Omega>m>0,$ $\chi$ is compactly supported and [F(x) = p|x|^{p-1} & if |x|>0 0 & if x=0.] with $p\in(0,1),$ under some restrictions on the parameters $p$ and $\Omega.$ We study also the behavior of the solutions as $p$ tends to zero to establish the link between these equations and the M.I.T. bag model ones.

View original: http://arxiv.org/abs/1208.2453