Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Bakhtina Z. I. On Stilties Differential on Time Scales. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 2, pp. 3-5. DOI: 10.18500/1816-9791-2009-9-2-3-5

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
18.06.2009
Full text:
(downloads: 144)
Language: 
Russian
Heading: 
UDC: 
517.927

On Stilties Differential on Time Scales

Autors: 
Bakhtina Zhanna Igorevna, Voronezh State University
Abstract: 

In this paper we apply the method of Stilties differentials offered by U.V. Pokornyi to the theory of Dynamic Equations on Time Scales. It’s possibly to put this theory on serious mathematical basis.

References: 
  1. Покорный Ю.В., Зверева М.Б., Шабров С.А. Осцилляционная теория Штурма – Лиувилля для импульсных задач // Успехи мат. наук. 2008. Т. 63, вып. 1(379). С. 111–154.
  2. Бодин С., Бохнер М., Лутц Д. Асимптотическое поведение решений динамических уравнений // Совр. мат. Фундаментальные направления. 2003. Т. 1. С. 30–39.
  3. Saker S.H. Oscillation of Second-Order Forced Nonlinear Dynamic Equations on Time Scales // Electronic J. of Qualitative Theory of Differential Equations. 2005. № 23. P. 1–17.
  4. Hilger S. Analysis on measure chains — a unified approach to continuous and discrete calculus // Results Math. 1990. V. 18. P. 18–56.
  5. Bohner M., Peterson A. Dynamic Equations on Time Scales: an Introduction with Applications. Boston: Birkh¨ auser Boston Inc., 2001. 358 с.
  6. Dosly O., Hilger S. A necessary and sufficient condition for oscillation of the Sturm Liouville dynamic equation on time scales // J. Comp. Appl. Math. 2002. V. 141. P. 147–158.
  7. Erbe L., Peterson A. Riccati equations on a measure chain // Dynamic systems and applications 3 (Atlanta, GA, 1999), Dynamic, Atlanta, GA, 2001. P. 193–199.