一类时滞依赖状态的集值抽象积分微分方程的可解性  

EXISTENCE RESULTS OF MULTI-VALUED ABSTRACT INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY VIA FRACTIONAL OPERATORS

作　　者：李文胜[1] 韩慧蓉[1] 周千[1] LI Wen-sheng HAN Hui-rong ZHOU Qian(School of Science, Xi＇an Aeronautical University, Xi＇an 710077, China)

机构地区：[1]西安航空学院理学院,陕西西安710077

出　　处：《数学杂志》2017年第2期347-357,共11页Journal of Mathematics

基　　金：国家自然科学基金资助(11161027);西安航空学院科研基金资助(2014KY1210)

摘　　要：本文研究了一类时滞依赖状态的集值抽象积分微分方程的可解性问题.利用集值映射不动点定理结合分析预解算子理论的方法,证明了上述微分方程温和解的存在性,推广了现有集值微分方程的结果.This paper is concerned with the existence of mild solutions for a multi-valued abstract integro-differential equations with state-dependent delay via fractional operators. By using the theories of a fixed point theorem for multivalued version combined with analytic resolvent operators, some existence theorems are proved. The result of multi-valued differential equations are extended.

关 键 词：分数阶算子 集值积分微分方程 时滞依赖状态 分析预解算子 

分 类 号：O175.22[理学—数学] O175.6[理学—基础数学]