Standing waves for semilinear Schrödinger equations with discontinuous dispersion

Abstract

We consider here semilinear Schrödinger equations with a non standard dispersion that is discontinuous at $$x=0$$ . We first establish the existence and uniqueness of standing wave solutions for these equations. We then study the orbital stability of these standing wave into a subspace of the energy space that where classical methods as the concentration-compactness method of P.L. Lions can be used.