本文選題：積分方程 + 時(shí)滯積分不等式　； 參考：《曲阜師范大學(xué)》2016年碩士論文

【摘要】：不等式是數(shù)學(xué)分支的主要研究內(nèi)容,在數(shù)學(xué)各領(lǐng)域都占據(jù)著非常重要的地位,其中積分不等式又是不等式的一個(gè)重要分支.在很多方程的理論研究中,雖然多數(shù)微分方程無法求出精確的解,但可以通過積分不等式對(duì)方程的解進(jìn)行估計(jì),進(jìn)而分析解的一些性質(zhì).近幾十年,隨著對(duì)積分方程和微分方程的的不斷研究,積分不等式和微分不等式也引起了學(xué)者的興趣,并得到了大量的結(jié)果,這些結(jié)果為研究積分方程,差分方程,微分方程,等各類方程的解的有界性、唯一性、存在性、穩(wěn)定性等性質(zhì)起了非常重要的作用.從1919年,Gronwall型不等式.1943年,Bellman推廣了Gronwall不等式,建立了Gronwall-Bellman型不等式.1956年Bihari把Gronwall-Bellman不等式從線性推廣到非線性.1973年P(guān)achpatte也建立了一系列不等式.近些年,這些不等式被許多學(xué)者進(jìn)一步研究和推廣,從一元推廣到二元,多元,從非時(shí)滯推廣到時(shí)滯,從連續(xù)推廣到非連續(xù).在這些不等式中,Gronwall-Bellman型不等式是最基礎(chǔ)，也是最重要的.根據(jù)內(nèi)容本文分為三部分：第一章本章中,在文獻(xiàn)[3]的基礎(chǔ)上,將文獻(xiàn)[3]的不等式進(jìn)行推廣.如將推廣到第二章本章中,在文獻(xiàn)[3][15]的基礎(chǔ)上,把其中推廣的時(shí)滯積分不等式推廣到二元的時(shí)滯積分不等式,如第三章本章中,在文獻(xiàn)[32]的基礎(chǔ)上,我們推廣了一類更為廣泛的不連續(xù)函數(shù)的積分不等式,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.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O178

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 孟東沅;孟凡偉;;一類新型具有兩個(gè)獨(dú)立變量的不連續(xù)函數(shù)的積分不等式[J];系統(tǒng)科學(xué)與數(shù)學(xué);2009年04期

2 ;A GENERALIZATION OF A RETARDED INEQUALITY AND ITS APPLICATIONS[J];Annals of Differential Equations;2006年01期

3 kP杴亮;;關(guān)于二階微分方程y″+A(t)y=0的解的有界性[J];數(shù)學(xué)進(jìn)展;1957年03期

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本文編號(hào)：1996939