Second type Hukuhara differentiable solutions to the delay set-valued differential equations

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• 作者：Marek T. Malinowski ^{m.malinowski@wmie.uz.zgora.pl}
• 关键词：Set differential equation ; Set differential equation with delay ; Existence and uniqueness of solution ; Second type Hukuhara derivative ; Hukuhara difference ; Set-valued mapping
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 May, 2012
• 卷：218
• 期：18
• 页码：9427-9437
• 文件大小：305 K

摘要

In this paper we consider the delay set-valued differential equations with a recently introduced notion of a second type Hukuhara derivative. Under condition that the right-hand side of the equation is Lipschitzian in the functional variable we obtain the existence and uniqueness of the solution to such the equations. Some properties of the solutions are established. Existence of at least one solution is also proved. Application of the second type Hukuhara differentiability concept to the problems of set-valued differential equations implies that the diameter of the solution values is a function nonincreasing in time.