混合型半线性积分-微分方程周期温和解存在性  

Existence of Periodic Mild Solutions for Mixed Semilinear Integral-Differential Equations

作　　者：王翰林 沈钦锐 WANG Hanlin;SHEN Qinrui(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《莆田学院学报》2025年第2期19-23,共5页Journal of putian University

基　　金：国家自然科学基金资助项目(11801255);福建省自然科学基金面上项目(2020J01798)。

摘　　要：为获取混合型半线性积分-微分方程周期温和解的存在性,应用算子半群理论,在特定的条件下(给定的函数和映射在其对应的集合上满足相应的Lipschitz条件,同时满足其他假设),借助算子连续、等度连续以及锥压缩不动点定理,证明了一类混合型半线性积分-微分方程周期温和解在Banach空间中存在。获取了该方程存在周期温和解的一些结果,并将结果作用于一个生态系统模型。In order to obtain the existence of periodic mild solutions for mixed semilinear integral-differential equations,using the operator semigroup theory,under the conditions that the given functions and mappings satisfy the corresponding Lipschitz conditions on their corresponding sets and other assumptions,with the help of operator continuity,equicontinuity and the cone compression fixed-point theorem,it is proved that the periodic mild solutions of a class of mixed semilinear integral-differential evolution equations exist in Banach spaces.Some results on the existence of periodic mild solutions of the equation are obtained,and the results are applied to an ecosystem model.

关 键 词：混合型半线性积分-微分方程 算子半群 锥压缩不动点定理 周期温和解 

分 类 号：O175.6[理学—数学]