Existence of nodal solutions for Dirac equations with singular nonlinearities - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales Henri Poincaré Année : 2012

Existence of nodal solutions for Dirac equations with singular nonlinearities

Résumé

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 \begin{equation*} i\underset{\mu=0}{\overset{3}{\sum}} \gamma^\mu \partial_\mu \psi- m\psi - F(\overline{\psi}\psi)\psi = 0 \end{equation*} where $\Omega>m>0,$ $\chi$ is compactly supported and \[ F(x) = \left\{\begin{array}{ll} p|x|^{p-1} & \text{if}~ |x|>0\\ 0 & \text{if}~ x=0 \end{array}\right. \] 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.
Fichier principal
Vignette du fichier
maincorrige.pdf (2.68 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00605824 , version 1 (06-07-2011)
hal-00605824 , version 2 (11-08-2012)
hal-00605824 , version 3 (18-01-2013)

Identifiants

Citer

Loïc Le Treust. Existence of nodal solutions for Dirac equations with singular nonlinearities. Annales Henri Poincaré, 2012, http://link.springer.com/article/10.1007/s00023-012-0224-6. ⟨10.1007/s00023-012-0224-6⟩. ⟨hal-00605824v3⟩
200 Consultations
190 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More