Existence of basic solutions of first order linear homogeneous set-valued differential equations

Q3 Mathematics Matematychni Studii Pub Date : 2024-03-19 DOI:10.30970/ms.61.1.61-78
A. Plotnikov, T. A. Komleva, N. Skripnik
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Abstract

The paper presents various derivatives of set-valued mappings,their main properties and how they are related to each other.Next, we consider Cauchy problems with linear homogeneousset-valued differential equations with different types ofderivatives (Hukuhara derivative, PS-derivative andBG-derivative). It is known that such initial value problems withPS-derivative and BG-derivative have infinitely many solutions.Two of these solutions are called basic. These are solutions suchthat the diameter function of the solution section is amonotonically increasing (the first basic solution) or monotonicallydecreasing (the second basic solution) function. However, the secondbasic solution does not always exist. We provideconditions for the existence of basic solutions of such initialvalue problems. It is shown that their existence depends on thetype of derivative, the matrix of coefficients on the right-handand the type of the initial set. Model examples are considered.
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一阶线性均质集值微分方程基本解的存在性
本文介绍了各种集值映射的导数、它们的主要性质以及它们之间的关系。接下来,我们考虑了具有不同类型导数(Hukuhara 导数、PS-导数和 BG-导数)的线性同构集值微分方程的 Cauchy 问题。众所周知,这种具有 PS 衍射和 BG 衍射的初值问题有无穷多个解。其中两个解称为基本解,即解部分的直径函数为单调递增函数(第一个基本解)或单调递减函数(第二个基本解)。然而,第二基本解并不总是存在。我们为此类初值问题基本解的存在提供了条件。结果表明,它们的存在取决于导数的类型、右侧系数矩阵和初始集的类型。考虑了模型实例。
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来源期刊
Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
期刊最新文献
On the h-measure of an exceptional set in Fenton-type theorem for Taylor-Dirichlet series Almost periodic distributions and crystalline measures Reflectionless Schrodinger operators and Marchenko parametrization Existence of basic solutions of first order linear homogeneous set-valued differential equations Real univariate polynomials with given signs of coefficients and simple real roots
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