Variational and topological methods for the study of nonlinear models from relativistic quantum mechanics.
This thesis is devoted to the study of nonlinear models from relativistic quantum mechanics.In the first part, we show thanks to a shooting method, the existence of infinitely many solutions of nonlinear Dirac equations of two models from the physics of hadrons and the physics of the nucleus.In the second part, we prove thanks to variational methods the existence of a ground state and excited states for two models of the physics of hadrons. Next, we study the phase transition which links the models thanks to the Γ-convergence.The last part is devoted to the study of another model from the physics of hadrons in which the wave functions are perfectly confined. We give some preliminary results.