Author(s)

Yolanda Silvia Santiago Ayala

Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Peru.

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Semigroups Theory, Weakly Continuous Operators, Existence of Solution, Generalized Schrödinger Equation, Distributional Problem, Periodic Distributional Space

Ayala, Y. (2023) Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation. Journal of Applied Mathematics and Physics, 11, 1061-1076. doi: 10.4236/jamp.2023.114070.