Uniqueness theorem in weighted Sobolev spaces of the Cauchy problem for Schrödinger type equations with variable coefficients

Abstract

The present paper is concerned with the uniqueness of solutions to the Cauchy problem for the Schrödinger type equations with variable coefficients. It is proved by the wellposedness of the associated adjoint problem that there is a unique solution to the Cauchy problem in exponentially weighted Sobolev spaces. The result, in this paper, is a natural generalization of that in the previous work.