
Existence of Nodal Solutions for Dirac Equations with Singular Nonlinearities
Le Treust, Loïc (2013), Existence of Nodal Solutions for Dirac Equations with Singular Nonlinearities, Annales Henri Poincaré, 14, 5, p. 1383-1411. http://dx.doi.org/10.1007/s00023-012-0224-6
View/ Open
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00605824/fr/Date
2013Journal name
Annales Henri PoincaréVolume
14Number
5Publisher
Springer
Pages
1383-1411
Publication identifier
Metadata
Show full item recordAbstract (EN)
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.Subjects / Keywords
Exited states; M.I.T. bag model; Winding number; Shooting method; Nodal solutionsRelated items
Showing items related by title and author.
-
Le Treust, Loïc (2013-07-05) Thèse
-
Manásevich, Raul; Garcia-Huidobro, Marta; Dolbeault, Jean (2013) Article accepté pour publication ou publié
-
Ishii, Hitoshi; Lions, Pierre-Louis; Arisawa, Mariko (2000) Article accepté pour publication ou publié
-
Burtea, Cosmin; Haspot, Boris (2020) Article accepté pour publication ou publié
-
Manásevich, Raul; Garcia-Huidobro, Marta; Dolbeault, Jean; Cortázar, Carmen (2014) Article accepté pour publication ou publié