Existence and stability results on a class of nonlinear Schrödinger equations in bounded domains with Dirichlet boundary conditions

Existence of solution, and L2 and H1 localization results on a class of nonlinear Schrödinger type equations with a bounded nonlinearity are obtained, for a bounded domain and with Dirichlet boundary conditions. The kind of stability under discussion shows that the corresponding solution exhibits features of a solitary wave type