Preliminaries The linear Schrodinger equation The Cauchy problem in a general domain The local Cauchy problem Regularity and the smoothing effect Global existence and finite-time blowup Asymptotic… Expand

We present a general method which enables us to prove the orbital stability of some standing waves in nonlinear Schrödinger equations. For example, we treat the cases of nonlinear Schrödinger… Expand

AbstractWe consider global solutions of the nonlinear Schrödinger equation(NLS)
$$iu_t + \Delta u = \lambda |u|^\alpha u, in R^N ,$$
where λ∈R and
$$0< \alpha< \frac{4}{{N - 2}}$$
. In particular,… Expand

We consider the initial value problem for the nonlinear Schrödinger equation in H1(Rn). We establish local existence and uniqueness for a wide class of subcritical nonlinearities. The proofs make use… Expand