几类泛函微分与积分方程的概周期性

发布时间：2018-05-12 12:23

本文选题：泛函微分方程 + 泛函积分方程　；参考：《江西师范大学》2015年硕士论文

【摘要】：本文主要研究了几类泛函微分与积分方程概周期解的存在性和稳定性,全文共分为六章.在第一章中,介绍了本文的研究背景和研究的主要问题.第二章作为预备知识,给出了概周期函数、(等度)渐近概周期函数的定义和基本性质.在第三章中,我们利用指数型二分性、压缩映像原理等方法,研究了一类Nicholson飞蝇模型概周期解的存在性与稳定性.在第四章中,在和不满足全局Lipschiz条件的情形下,探讨了一类细胞神经网络模型概周期解的存在性与稳定性.在第五章中,我们首先给出了(等度)渐近概周期函数的一些性质,然后研究了一类泛函积分方程渐近概周期解的存在性.在第六章中,我们利用混合单调算子不动点定理,建立了一类造血模型概周期解的存在性定理.
[Abstract]:In this paper, we mainly study the existence and stability of almost periodic solutions of functional differential and integral equations. The full text is divided into six chapters. In the first chapter, the research background and main problems of this paper are introduced. The second chapter, as a preparatory knowledge, gives the definition and basic properties of almost periodic function, (isometric) asymptotically almost periodic function. In the three chapter, we study the existence and stability of almost periodic solutions for a class of Nicholson fly models by means of exponential two division and compression mapping principle. In the fourth chapter, the existence and stability of almost periodic solutions for a kind of cellular neural network model are discussed in the case of and not satisfying the global Lipschiz condition. In the fifth chapter, the existence and stability of the almost periodic solution of a kind of cellular neural network model are discussed. We first give some properties of asymptotically almost periodic functions, and then study the existence of asymptotically almost periodic solutions for a class of functional integral equations. In the sixth chapter, we use the fixed point theorem of mixed monotone operator to establish the existence and existence theorem of almost periodic solutions for a class of hematopoietic models.

【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

【共引文献】