Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Cover of the book

2019 | OriginalPaper | Chapter

2. Analysis of Continuous Equations

Author : Anatoly A. Martynyuk

Published in: Qualitative Analysis of Set-Valued Differential Equations

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter the application of the comparison principle and the direct Lyapunov method in terms of auxiliary matrix-valued functions is proposed for solution of the problems under consideration.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Literature
2.
Aleksandrov, A.Yu., Platonov, A.V.: Aggregation and stability analysis of nonlinear complex systems. J. Math. Anal. Appl. 342(2), 989–1002 (2008)MathSciNetCrossRef
20.
Corduneanu, C., Li, Y., Mehran, M.: Functional Differential Equations: Advances and Applications. Wiley, New York (2016)CrossRef
25.
Djordjevic̀, M.Z.: Zur Stabilitat Nichtlinearer Gekoppelter Systeme mit der Matrix-Ljapunov-Methode. Diss. ETH 7690, Zurich (1984)
28.
Gajic, Z.: Quantitative methods in nonlinear dynamics: novel approaches to Liapunov’s matrix functions by A. A. Martynyuk, New York: Marcel Dekker, 2002. Int. J. Robust Nonlinear Control 16, 465–466 (2006)CrossRef
31.
Hahn, W.: Stability of Motion. Springer, Berlin (1995)
35.
Hyers, D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. U. S. A. 27, 222–224 (1941)MathSciNetCrossRef
36.
Hyers, D.H., Isac, G., Rassias, Th.M.: Stability of Functional Equations in Several Variables. Birkhauser Verlag, Boston (1998)CrossRef
38.
Kats, I.Ya., Martynyuk, A.A.: Stability and Stabilization of Nonlinear Systems with Random Structure. Stability and Control: Theory, Methods and Applications, vol. 18. Taylor and Francis, London (2002)
49.
Lakshmikantham, V., Bhaskar, T.G., Vasundhara Devi, J.: Theory of Set Differential Equations in Metric Spaces. Cambridge Scientific Publishers, Cambridge (2006)MATH
51.
Lakshmikantham, V., Leela, S., Martynyuk, A.A.: Stability Analysis of Nonlinear Systems, 2nd edn. Springer, Basel (2015)CrossRef
53.
Lyapunov, A.M.: The General Problem of the Stability of Motion. GITTL, Moscow (1950)
64.
Martynyuk, A.A.: Stability by Liapunov’s Matrix Function Method with Applications. Marcel Dekker, New York (1998)
66.
Martynyuk, A.A.: Qualitative Methods in Nonlinear Dynamics. Novel Approaches to Liapunov’s Matrix Function. Marcel Dekker, New York (2002)
69.
Martynyuk, A.A.: Stability of Motion. The Role of Multicomponent Liapunov’s Functions. Cambridge Scientific Publishers, Cambridge (2007)
70.
72.
Martynyuk, A.A.: Asymptotic stability criterion for nonlinear monotonic systems and its applications (Review). Int. Appl. Mech. 47(5), 475–534 (2011)MathSciNetCrossRef
82.
Martynyuk, A.A., Obolenskij, A.Yu.: Stability of solutions of autonomous Wazewskij systems. Differ. Equ. 16(8), 1392–1407 (1980)
83.
Martynyuk, A.A., Martynyuk-Chernienko, Yu.A.: Uncertain Dynamical Systems: Stability and Motion Control. CRC Press Taylor and Francis Group, Boca Raton (2012)MATH
85.
Martynyuk, A.A., Martynyuk-Chernienko, Yu.A.: Analysis of the set of trajectories nonlinear dynamics: stability and boundedness of motions. Differ. Equ. 49(1), 20–31 (2013)MathSciNetCrossRef
89.
Martynyuk, A.A., Miladzhanov, V.G.: Stability Analysis of Nonlinear Systems Under Structural Perturbations. Cambridge Scientific Publishers, Cambridge (2014)MATH
91.
Martynyuk, A.A., Chernetskaya, L.N., Martynyuk-Chernienko, Yu.A.: Dynamic analysis of the trajectories on product of convex compacts. Dokl. NAS Ukr. 9, 44–50 (2016)MATH
103.
106.
Rus, I.A.: Ulam stabilities of ordinary differential equations in a Banach space. Carpathian J. Math. 26(1), 103–107 (2010)MathSciNetMATH
109.
Shurz, H.: Stability by Lyapunov’s Matrix Function Method with Applications by Martynyuk A.A. Pure and Applied Mathematics, vol. 214. Marcel Dekker, New York (1998). Zentralblatt MATH 907, 166–167
115.
Ulam, S.M.: A Collection of the Mathematical Problems. Interscience Publ., New York (1960)MATH
119.
Walter, W.: Differential and Integral Inequalities. Springer, Berlin (1970)CrossRef
122.
Yoshizawa, T.: Stability Theory by Liapunov’s Second Method. Mathematics Society Japan, Tokyo (1966)
123.
Zaremba, S.K.: Sur les equations au paratingent. Bull. Sci. Math. bfLX(2), 139–160 (1936)
Metadata
Title
Analysis of Continuous Equations
Author
Anatoly A. Martynyuk
Copyright Year
2019
Book
Qualitative Analysis of Set-Valued Differential Equations

Print ISBN: 978-3-030-07643-6

Electronic ISBN: 978-3-030-07644-3

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-07644-3_2