Existence of solution of a distributional problem for a generalized Schrödinger equation
Keywords:Groups theory, existence of solution, Schrödinger equation, distributional problem, weakly continuous operators
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.
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