本文關(guān)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(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：近年來(lái),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(guó)內(nèi)外學(xué)者的廣泛關(guān)注.集值微分方程作為常微分方程的推廣之一,在物理學(xué)、生物學(xué)和工程學(xué)中有許多應(yīng)用.然而由于集值微分方程自身的復(fù)雜性,其定性與穩(wěn)定性問(wèn)題的相關(guān)結(jié)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(wèn)題.全文分為以下三部分內(nèi)容:第一部分在右端函數(shù)滿足較弱條件下,利用廣義擬線性化方法,獲得函數(shù)項(xiàng)為三項(xiàng)和的集值微分方程初值問(wèn)題解的平方收斂性.第二部分在右端函數(shù)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(xiàng)的集值微分方程周期邊值問(wèn)題解的平方收斂性.第三部分在右端函數(shù)滿足一定條下,通過(guò)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(wèn)題解的高階收斂性;以及在右端函數(shù)分別滿足超凸或超凹的條件下,通過(guò)引入耦合上下解的定義,證明函數(shù)項(xiàng)為兩項(xiàng)和的集值微分方程初值問(wèn)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(xué)位授予單位】：河北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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相關(guān)期刊論文 前2條

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本文編號(hào)：1463869