發(fā)布時間：2018-01-25 22:29

  本文關鍵詞： 集值微分方程 上下解方法 擬線性化方法 平方收斂 高階收斂　出處：《河北大學》2017年碩士論文　論文類型：學位論文

【摘要】：近年來,定義在半線性度量空間上的集值微分方程的研究引起了國內外學者的廣泛關注.集值微分方程作為常微分方程的推廣之一,在物理學、生物學和工程學中有許多應用.然而由于集值微分方程自身的復雜性,其定性與穩(wěn)定性問題的相關結果還不多.本文主要利用擬線性化方法,討論幾種類型的集值微分方程解的收斂性問題.全文分為以下三部分內容:第一部分在右端函數滿足較弱條件下,利用廣義擬線性化方法,獲得函數項為三項和的集值微分方程初值問題解的平方收斂性.第二部分在右端函數滿足一定的條件下,證明比較定理,利用擬線性化方法,討論具有最大項的集值微分方程周期邊值問題解的平方收斂性.第三部分在右端函數滿足一定條下,通過引入超凸超凹的定義,利用擬線性化方法,研究集值微分方程初值問題解的高階收斂性;以及在右端函數分別滿足超凸或超凹的條件下,通過引入耦合上下解的定義,證明函數項為兩項和的集值微分方程初值問題的高階收斂性.
[Abstract]:In recent years, the study of set-valued differential equations defined on semilinear metric spaces has attracted wide attention of scholars at home and abroad. As one of the generalizations of ordinary differential equations, set-valued differential equations are widely used in physics. There are many applications in biology and engineering. However, due to the complexity of set-valued differential equations, there are few results related to their qualitative and stability problems. This paper discusses the convergence of solutions of several types of set-valued differential equations. This paper is divided into the following three parts: in the first part, the generalized quasi-linearization method is used to satisfy the weak condition of the right end function. The quadratic convergence of the solution of the initial value problem of set-valued differential equations with a trisomponent term is obtained. In the second part, the comparison theorem is proved and the quasi-linearization method is used under the condition that the function at the right end satisfies certain conditions. The quadratic convergence of solutions of periodic boundary value problems for set-valued differential equations with the largest term is discussed. In the third part, by introducing the definition of hyperconvex hyperconcave, the quasi-linearization method is used. The higher order convergence of solutions for initial value problems of set-valued differential equations is studied. By introducing the definition of coupled upper and lower solutions, the higher order convergence of the initial value problem of set-valued differential equations with binomial terms is proved under the condition that the right end function satisfies hyperconvex or hyperconcave, respectively.
【學位授予單位】：河北大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

【參考文獻】

相關期刊論文 前2條

1 王培光;劉靜;李志芳;;集值控制微分方程解的廣義擬線性方法[J];黑龍江大學自然科學學報;2011年02期

2 王培光;高瑋;;集值微分方程初值問題的擬線性化方法[J];河北大學學報(自然科學版);2011年01期

，

本文編號：1463869