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Qualitative Analysis of Set-Valued Differential Equations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Qualitative Analysis of Set-Valued Differential Equations/ by Anatoly A. Martynyuk.
Author:	Martynyuk, Anatoly A.
Description:	XIII, 198 p. 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Differential equations. -
Online resource:	https://doi.org/10.1007/978-3-030-07644-3
ISBN:	9783030076443

Qualitative Analysis of Set-Valued Differential Equations
Martynyuk, Anatoly A.

Qualitative Analysis of Set-Valued Differential Equations[electronic resource] /by Anatoly A. Martynyuk. - 1st ed. 2019. - XIII, 198 p. 1 illus. in color.online resource.

General Properties of Set Equations -- Analysis of the Set of Continuous Equations -- Stability of the Set of Discrete–Time Systems -- Qualitative Analysis of Set Impulsive Equations -- Stability of Set Systems with Aftereﬀect -- Analysis of Set Impulsive Systems with Aftereﬀect -- Stability of Set Equations with Causal Operator -- Finite-Time Stability of Standard Systems Sets.

The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the ﬁeld of qualitative analysis of differential and other types of equations.

ISBN: 9783030076443

Standard No.: 10.1007/978-3-030-07644-3doiSubjects--Topical Terms:

527664
Differential equations.

LC Class. No.: QA372

Dewey Class. No.: 515.352

Qualitative Analysis of Set-Valued Differential Equations
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505 0 $a General Properties of Set Equations -- Analysis of the Set of Continuous Equations -- Stability of the Set of Discrete–Time Systems -- Qualitative Analysis of Set Impulsive Equations -- Stability of Set Systems with Aftereﬀect -- Analysis of Set Impulsive Systems with Aftereﬀect -- Stability of Set Equations with Causal Operator -- Finite-Time Stability of Standard Systems Sets.
520 $a The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the ﬁeld of qualitative analysis of differential and other types of equations.
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