几类新的积分不等式研究

发布时间：2018-04-21 03:26

本文选题：积分不等式 + 弱奇异核　；参考：《曲阜师范大学》2017年硕士论文

【摘要】：微分方程,积分方程及差分方程在数学、物理、医疗、光学、动力系统等领域发挥了重要作用.许多学者对方程的性质进行了多方面的研究,其中,Gronwall型、Wendroff型积分不等式等一些弱奇异积分不等式在微分方程性质的研究中是非常重要的工具.这篇文章里将建立新的Gronwall型、Wendroff、Henry型等弱奇异积分不等式,并给出它们在微分方程解的唯一性、有界性和对初值连续依赖性等性质研究方面的应用.本文在参考文献[13,14,15,23,24,30]的基础上,将相关积分不等式进行推广,并得到一些新的结果.根据内容本文分为以下四章:第一章绪论,介绍本文研究的主要问题及其背景.第二章结合参考文献[15]中一些已知的积分不等式,研究积分不等式:第三章研究一些新的Wendroff型不等式,推广到如下的含有两个变元的积分不等式:第四章研究如下形式的Henry型弱奇异积分不等式:
[Abstract]:Differential equations, integral equations and differential equations play an important role in the fields of mathematics, physics, medicine, optics, dynamic systems and so on. Many scholars have studied the properties of the equation in many aspects. Some weak singular integral inequalities such as Gronwall type Wendroff type integral inequalities are very important tools in the study of differential equation properties. In this paper, new weak singular integral inequalities of Gronwall type Wendroff-Henry type are established, and their applications in the study of uniqueness, boundedness and continuous dependence on initial values of differential equations are given. On the basis of reference [13 / 14 / 15 / 23 / 24 / 30], this paper generalizes the relevant integral inequalities and obtains some new results. According to the content, this paper is divided into four chapters: the first chapter introduces the main problems and background of this study. In the second chapter, some known integral inequalities in reference [15] are studied. In chapter three, some new Wendroff type inequalities are studied. We generalize the following integral inequalities with two variables: in Chapter 4, we study the following forms of weakly singular integral inequalities of Henry type:
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O178

【参考文献】