Top

Published in:

2015 | OriginalPaper | Chapter

10. Asymptotics for Dynamic Equations on Time Scales

Authors : Sigrun Bodine, Donald A. Lutz

Published in: Asymptotic Integration of Differential and Difference Equations

Publisher: Springer International Publishing

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

search-config

AI-assisted search

Off

Abstract

In the foregoing chapters, one sees that many asymptotic results for linear differential and difference equations as well as the methods used to derive them are closely related. So it is natural to ask for a framework which would encompass both sets of results as well as including some generalizations. One possibility for doing this has been discussed by Spigler and Vianello [143].

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

previous chapter Applications to Classes of Scalar Linear Difference Equations

12.

S. Bodine, D.A. Lutz, Exponential functions on time scales: their asymptotic behavior and calculation. Dyn. Syst. Appl. 12, 23–43 (2003)MATHMathSciNet

16.

S. Bodine, D.A. Lutz, A Hartman-Wintner theorem for dynamic equations on time scales. J. Differ. Equ. Appl. 14, 1–16 (2008)CrossRefMATHMathSciNet

22.

S. Bodine, M. Bohner, D.A. Lutz, Asymptotic behavior of solutions of dynamic equations. Sovrem. Mat. Fundam. Napravl. 1, 30–39 (2003) (in Russian). Translation in J. Math. Sci. 124, 5110–5118 (2004)

23.

M. Bohner, D.A. Lutz, Asymptotic behavior of dynamic equations on time scales. J. Differ. Equ. Appl. 7, 21–50 (2001)CrossRefMATHMathSciNet

24.

M. Bohner, D.A. Lutz, Asymptotic expansions and analytic dynamic equations. Z. Angew. Math. Mech. 86, 37–45 (2006)CrossRefMATHMathSciNet

25.

M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications (Birkhäuser, Boston, 2001)CrossRef

26.

M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales (Birkhäuser, Boston, 2003)CrossRefMATH

69.

W.A. Harris, D.A. Lutz, On the asymptotic integration of linear differential systems. J. Math. Anal. Appl. 48, 1–16 (1974)CrossRefMATHMathSciNet

75.

S. Hilger, Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)CrossRefMATHMathSciNet

108.

R. Mert, A. Zafer, Time scale extensions of a theorem of Wintner on systems with asymptotic equilibrium. J. Differ. Equ. Appl. 17, 841–857 (2011)CrossRefMATHMathSciNet

132.

G. Ren, Y. Shi, Asymptotic behaviour of dynamic systems on time scales. J. Differ. Equ. Appl. 12, 1289–1302 (2006)CrossRefMATHMathSciNet

143.

R. Spigler, M. Vianello, Discrete and continuous Liouville–Green–Olver approximations: a unified treatment via Volterra-Stieltjes integral equations. SIAM J. Math. Anal. 25, 720–732 (1994)CrossRefMATHMathSciNet

152.

W. Trench, Extensions of a theorem of Wintner on systems with asymptotically constant solutions. Trans. Am. Math. Soc. 293, 477–483 (1986)CrossRefMATHMathSciNet

Title: Asymptotics for Dynamic Equations on Time Scales
Authors: Sigrun Bodine
Donald A. Lutz
Publisher: Springer International Publishing
Book: Asymptotic Integration of Differential and Difference Equations
Print ISBN: 978-3-319-18247-6

Electronic ISBN: 978-3-319-18248-3

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-18248-3_10

Springer Professional

Abstract

Please log in to get access to your license.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner