一类线性微分方程的指数增长型伪概反自守解  

Existence and Uniqueness of a Class of Linear Differential Equation of Exponential Type Pseudo Almost Anti-automorphic Solution

作　　者：赵莉莉 ZHAO Lili(School of Mathematics and Statistics,Yunnan University,Kunming 650091,Yunan,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650091

出　　处：《惠州学院学报》2024年第3期64-72,共9页Journal of Huizhou University

基　　金：云南省教育厅自然科学基金项目(2020J0020);云南大学教育教学改革研究项目(2023Y22)。

摘　　要：为了探讨微分系统指数增长型伪概反自守温和解的相关动力学性质。首先,将伪概自守函数的概念推广到伪概反自守函数。其次,讨论了伪概反自守函数的相关性质,证明了全体伪概反自守函数构成的集合,在无穷范数下,成为一个Banach空间。最后,利用C_(0)-半群相关理论,得到一类线性微分方程具有指数增长型的伪概反自守温和解存在并且唯一的充分条件。To investigate the dynamic properties of pseudo almost anti-automorphic mild solutions of exponential growth type in differential systems,this paper proposes an extension of the concept of pseudo almost automorphic functions to pseudo almost anti-automorphic functions.The study delves into the properties of these functions and establishes that the set of all pseudo almost anti-automorphic functions forms a Banach space equipped with an infinite norm.Furthermore,by applying relevant semigroup theories,the paper derives sufficient conditions for the uniqueness and existence of pseudo almost anti-automorphic mild solutions to a class of linear differential equations exhibiting exponential growth.

关 键 词：线性微分方程 伪概反自守函数 温和解 C_(0)-半群 指数增长型 

分 类 号：O175.1[理学—数学]