Geodesic
On the Stieltjes Procedure for Closing Gaps in Time Scales
Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 733-735.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : dynamic equations on time scales
Keywords: discontinuous argument, Stieltjes integration, function of bounded variation. 
@article{MZM_2009_86_5_a9,
     author = {Yu. V. Pokornyi and Zh. I. Bakhtina},
     title = {On the {Stieltjes} {Procedure} for {Closing} {Gaps} in {Time} {Scales}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {733--735},
     publisher = {mathdoc},
     volume = {86},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a9/}
}
TY  - JOUR
AU  - Yu. V. Pokornyi
AU  - Zh. I. Bakhtina
TI  - On the Stieltjes Procedure for Closing Gaps in Time Scales
JO  - Matematičeskie zametki
PY  - 2009
SP  - 733
EP  - 735
VL  - 86
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a9/
LA  - ru
ID  - MZM_2009_86_5_a9
ER  - 
%0 Journal Article
%A Yu. V. Pokornyi
%A Zh. I. Bakhtina
%T On the Stieltjes Procedure for Closing Gaps in Time Scales
%J Matematičeskie zametki
%D 2009
%P 733-735
%V 86
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a9/
%G ru
%F MZM_2009_86_5_a9
Yu. V. Pokornyi; Zh. I. Bakhtina. On the Stieltjes Procedure for Closing Gaps in Time Scales. Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 733-735. http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a9/

[1] S. Bodin, M. Bone, D. Lutts, “Asimptoticheskoe povedenie reshenii dinamicheskikh uravnenii”, SMFN, 1 (2003), 30–39 | MR | Zbl

[2] S. Hilger, “Analysis on measure chains – a unified approach to continuous and discrete calculus”, Results Math., 18:1–2 (1990), 18–56 | MR | Zbl

[3] M. Bohner, A. Peterson, Dynamic Equations on Time Scales. An Introduction with Applications, Birkhäuser, Boston, MA, 2001 | MR | Zbl

[4] O. Došlý, 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 (2002), 147–158 | DOI | MR | Zbl

[5] 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, 17 pp | MR | Zbl

[6] Yu. V. Pokornyi, M. B. Zvereva, S. A. Shabrov, “Ostsillyatsionnaya teoriya Shturma–Liuvillya dlya impulsnykh zadach”, UMN, 63:1 (2008), 111–154 | MR | Zbl