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