發(fā)布時間：2018-04-21 03:26

  本文選題：積分不等式 + 弱奇異核�。� 參考：《曲阜師范大學(xué)》2017年碩士論文

【摘要】：微分方程,積分方程及差分方程在數(shù)學(xué)、物理、醫(yī)療、光學(xué)、動力系統(tǒng)等領(lǐng)域發(fā)揮了重要作用.許多學(xué)者對方程的性質(zhì)進(jìn)行了多方面的研究,其中,Gronwall型、Wendroff型積分不等式等一些弱奇異積分不等式在微分方程性質(zhì)的研究中是非常重要的工具.這篇文章里將建立新的Gronwall型、Wendroff、Henry型等弱奇異積分不等式,并給出它們在微分方程解的唯一性、有界性和對初值連續(xù)依賴性等性質(zhì)研究方面的應(yīng)用.本文在參考文獻(xiàn)[13,14,15,23,24,30]的基礎(chǔ)上,將相關(guān)積分不等式進(jìn)行推廣,并得到一些新的結(jié)果.根據(jù)內(nèi)容本文分為以下四章:第一章緒論,介紹本文研究的主要問題及其背景.第二章結(jié)合參考文獻(xiàn)[15]中一些已知的積分不等式,研究積分不等式:第三章研究一些新的Wendroff型不等式,推廣到如下的含有兩個變元的積分不等式:第四章研究如下形式的Henry型弱奇異積分不等式:
[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:
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O178

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 吳宇;唐敏;周察金;;一類新的弱奇性Wendroff型積分不等式解的估計(jì)[J];應(yīng)用數(shù)學(xué)學(xué)報;2013年01期

2 馬慶華,楊恩浩;弱奇性Volterra積分不等式解的估計(jì)[J];應(yīng)用數(shù)學(xué)學(xué)報;2002年03期

，

本文編號：1780736