几类时滞积分不等式的推广及应用

发布时间：2018-06-08 19:31

本文选题：积分方程 + 时滞积分不等式　；参考：《曲阜师范大学》2016年硕士论文

【摘要】：不等式是数学分支的主要研究内容,在数学各领域都占据着非常重要的地位,其中积分不等式又是不等式的一个重要分支.在很多方程的理论研究中,虽然多数微分方程无法求出精确的解,但可以通过积分不等式对方程的解进行估计,进而分析解的一些性质.近几十年,随着对积分方程和微分方程的的不断研究,积分不等式和微分不等式也引起了学者的兴趣,并得到了大量的结果,这些结果为研究积分方程,差分方程,微分方程,等各类方程的解的有界性、唯一性、存在性、稳定性等性质起了非常重要的作用.从1919年,Gronwall型不等式.1943年,Bellman推广了Gronwall不等式,建立了Gronwall-Bellman型不等式.1956年Bihari把Gronwall-Bellman不等式从线性推广到非线性.1973年Pachpatte也建立了一系列不等式.近些年,这些不等式被许多学者进一步研究和推广,从一元推广到二元,多元,从非时滞推广到时滞,从连续推广到非连续.在这些不等式中,Gronwall-Bellman型不等式是最基础，也是最重要的.根据内容本文分为三部分：第一章本章中,在文献[3]的基础上,将文献[3]的不等式进行推广.如将推广到第二章本章中,在文献[3][15]的基础上,把其中推广的时滞积分不等式推广到二元的时滞积分不等式,如第三章本章中,在文献[32]的基础上,我们推广了一类更为广泛的不连续函数的积分不等式,如.
[Abstract]:Inequality is the main research content of mathematics branch, which occupies a very important position in all fields of mathematics, in which integral inequality is an important branch of inequality. In the theoretical study of many equations, although most differential equations can not obtain exact solutions, we can estimate the solutions of the equations through integral inequalities, and then analyze some properties of the solutions. In recent decades, with the continuous study of integral equations and differential equations, integral inequalities and differential inequalities have aroused the interest of scholars, and a large number of results have been obtained, which are the study of integral equations, difference equations, differential equations. The boundedness, uniqueness, existence and stability of the solutions of all kinds of equations play a very important role. From 1919 to 1919, Bellman generalized Gronwall inequality and established Gronwall-Bellman inequality. In 1956, Bihari extended Gronwall-Bellman inequality from linear to nonlinear. In 1973, Pachpatte also established a series of inequalities. In recent years, these inequalities have been further studied and generalized by many scholars, from univariate to binary, multivariate, from non-delay to delay-delay, from continuous to discontinuous. Among these inequalities, Gronwall-Bellman type inequality is the most basic and important. This paper is divided into three parts according to the content: in Chapter 1, the inequality of [3] is generalized on the basis of reference [3]. If we generalize it to the second chapter, on the basis of [3] [15], we generalize the extended delay integral inequality to the binary delay integral inequality, as in Chapter 3, on the basis of [32], We generalize a class of integral inequalities for a more extensive discontinuous function, such as.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O178

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