Abstract
In the present paper, we show that the theory of dynamic equations on time scales (with an argument with “holes,” i.e., a discontinuous argument) can significantly be simplified and generalized by using Stieltjes integration, which is inverse to the differentiation with respect to Riesz measures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Bodine, M. Bohner, and D. Lutz, “Asymptotic behavior of solutions of dynamic equations,” Sovrem. Mat., Fundam. Napravl. 1, 30–39 (2003) [J. Math. Sci., New York 124 (4), 5110–5118 (2004)].
S. Hilger, “Analysis on measure chains — a unified approach to continuous and discrete calculus,” Results Math. 18(1–2), 18–56 (1990).
M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications (Birkhäuser, Boston, MA, 2001).
O. Došlý and S. Hilger, “A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales,” J.Comput. Appl. Math. 141(1–2), 147–158 (2002).
S. H. Saker, “Oscillation of second-order forced nonlinear dynamic equations on time scales,” Electron. J. Qual. Theory Differ. Equ. 2005 (2005), Paper No. 23.
Yu. V. Pokornyi, M. B. Zvereva, and S. A. Shabrov, “Sturm-Liouville oscillation theory for impulsive problems,” UspekhiMat. Nauk. 63(1), 111–154 (2008) [RussianMath. Surveys 63 (1), 109–153 (2008)].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu. V. Pokornyi, Zh. I. Bakhtina, 2009, published in Matematicheskie Zametki, 2009, Vol. 86, No. 5, pp. 733–735.
Rights and permissions
About this article
Cite this article
Pokornyi, Y.V., Bakhtina, Z.I. On the stieltjes procedure for closing gaps in time scales. Math Notes 86, 690–692 (2009). https://doi.org/10.1134/S000143460911011X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S000143460911011X