On unique continuation for the generalized Schrِdinger equations

In this paper, we study the unique continuation properties of solutions of the generalized Schrödinger equations. We prove the Carleman inequalities, as well as the exponential decay weighted estimates. As a consequence we obtain sufficient conditions on the behavior of the solution u at two different times t 0 = 0 and t 1 = 1 which guarantee that u ≡ 0 is the unique solution.