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

• Autor: Santiago Ayala, Yolanda
• Formato: artículo
• Fecha de Publicación: 2022
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/4390
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4390
• Nivel de acceso: acceso abierto
• Materia: Teoría de grupos; existencia de solución; ecuación de Schrödinger; problema distribucional; operadores debilmente continuos; 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.