Existence of solution of a distributional problem for a generalized Schrödinger equation

Abstract

In this article, we prove the existence and uniqueness of the solution of the homogeneous generalized Schrödinger equation of order m in the periodic distributional space P0, where m is an even number not a multiple of four. Furthermore, we prove that the solution depends continuously respect to the initial data in P0. Introducing a family of weakly continuous operators, we prove that this family is a group in P0. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give the conclusions and remarks derived from this study.

Keywords

• groups theory
• existence of solution
• schr¨odinger equation of order m
• distributional problem
• weakly continuous operators