國立高雄大學圖資館 |

Language: English

Back

Qualitative analysis of set-valued d...

Martynyuk, Anatoly A.

Qualitative analysis of set-valued differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Qualitative analysis of set-valued differential equationsby Anatoly A. Martynyuk.
Author:	Martynyuk, Anatoly A.
Published:	Cham :Springer International Publishing :2019.
Description:	xiii, 198 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equationsQualitative theory.
Online resource:	https://doi.org/10.1007/978-3-030-07644-3
ISBN:	9783030076443$q(electronic bk.)

Qualitative analysis of set-valued differential equations
Martynyuk, Anatoly A.

Qualitative analysis of set-valued differential equations[electronic resource] /by Anatoly A. Martynyuk. - Cham :Springer International Publishing :2019. - xiii, 198 p. :ill., digital ;24 cm.

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$q(electronic bk.)

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

328936
Differential equations
--Qualitative theory.

LC Class. No.: QA371

Dewey Class. No.: 515.35

Qualitative analysis of set-valued differential equations
LDR:02160nmm a2200325 a 4500 001 554733
003 DE-He213
005 20190401170601.0
006 m d
007 cr nn 008maaau
008 191118s2019 gw s 0 eng d
020 $a 9783030076443$q(electronic bk.)
020 $a 9783030076436$q(paper)
024 7 $a 10.1007/978-3-030-07644-3 $2 doi
035 $a 978-3-030-07644-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA371
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA371 $b .M388 2019
100 1 $a Martynyuk, Anatoly A. $3 732755
245 1 0 $a Qualitative analysis of set-valued differential equations $h [electronic resource] / $c by Anatoly A. Martynyuk.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xiii, 198 p. : $b ill., digital ; $c 24 cm.
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.
650 0 $a Differential equations $x Qualitative theory. $3 328936
650 1 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Systems Theory, Control. $3 274654
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-07644-3
950 $a Mathematics and Statistics (Springer-11649)