Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation  

作　　者：Yolanda Silvia Santiago Ayala Yolanda Silvia Santiago Ayala(Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Peru)

机构地区：[1]Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, Peru

出　　处：《Journal of Applied Mathematics and Physics》2023年第4期1061-1076,共16页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Semigroups Theory Weakly Continuous Operators Existence of Solution Generalized Schrödinger Equation Distributional Problem Periodic Distributional Space 

分 类 号：O17[理学—数学]