Some notes on oscillation of two-dimensional system of difference equations
Mathematica Bohemica (2014)
- Volume: 139, Issue: 2, page 417-428
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topOpluštil, Zdeněk. "Some notes on oscillation of two-dimensional system of difference equations." Mathematica Bohemica 139.2 (2014): 417-428. <http://eudml.org/doc/261894>.
@article{Opluštil2014,
abstract = {Oscillatory properties of solutions to the system of first-order linear difference equations \[ \begin\{aligned\} \Delta u\_k & = q\_k v\_k \\ \Delta v\_k & = -p\_k u\_\{k+1\}, \end\{aligned\} \]
are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).},
author = {Opluštil, Zdeněk},
journal = {Mathematica Bohemica},
keywords = {two-dimensional system; linear difference equation; oscillatory solution; linear difference system; oscillatory solution},
language = {eng},
number = {2},
pages = {417-428},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some notes on oscillation of two-dimensional system of difference equations},
url = {http://eudml.org/doc/261894},
volume = {139},
year = {2014},
}
TY - JOUR
AU - Opluštil, Zdeněk
TI - Some notes on oscillation of two-dimensional system of difference equations
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 2
SP - 417
EP - 428
AB - Oscillatory properties of solutions to the system of first-order linear difference equations \[ \begin{aligned} \Delta u_k & = q_k v_k \\ \Delta v_k & = -p_k u_{k+1}, \end{aligned} \]
are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).
LA - eng
KW - two-dimensional system; linear difference equation; oscillatory solution; linear difference system; oscillatory solution
UR - http://eudml.org/doc/261894
ER -
References
top- Agarwal, R. P., Difference Equations and Inequalities: Theory, Methods and Applications, Pure and Appl. Math. Marcel Dekker, New York (1992). (1992) Zbl0925.39001MR1155840
- Chantladze, T., Kandelaki, N., Lomtatidze, A., 10.1023/A:1022911815254, Georgian Math. J. 6 (1999), 401-414. (1999) Zbl0944.34025MR1692963DOI10.1023/A:1022911815254
- Hartman, P., Ordinary Differential Equations, John Wiley, New York (1964). (1964) Zbl0125.32102MR0171038
- Hille, E., 10.1090/S0002-9947-1948-0027925-7, Trans. Am. Math. Soc. 64 (1948), 234-252. (1948) Zbl0031.35402MR0027925DOI10.1090/S0002-9947-1948-0027925-7
- Lomtatidze, A., 10.1023/A:1022978000000, Georgian Math. J. 4 (1997), 129-138. (1997) Zbl0877.34029MR1439591DOI10.1023/A:1022978000000
- Lomtatidze, A., Partsvania, N., 10.1023/A:1022187214750, Georgian Math. J. 6 (1999), 285-298. (1999) Zbl0930.34025MR1679448DOI10.1023/A:1022187214750
- Nehari, Z., 10.1090/S0002-9947-1957-0087816-8, Trans. Am. Math. Soc. 85 (1957), 428-445. (1957) Zbl0078.07602MR0087816DOI10.1090/S0002-9947-1957-0087816-8
- Opluštil, Z., Oscillatory criteria for two-dimensional system of difference equations, Tatra Mt. Math. Publ. 48 (2011), 153-163. (2011) Zbl1265.39019MR2841115
- Polák, L., Oscillation and nonoscillation criteria for two-dimensional systems of linear ordinary differential equations, Georgian Math. J. 11 (2004), 137-154. (2004) Zbl1064.34019MR2065547
- Wintner, A., 10.1090/qam/28499, Q. Appl. Math. 7 (1949), 115-117. (1949) Zbl0032.34801MR0028499DOI10.1090/qam/28499
- Wintner, A., 10.2307/2372182, Am. J. Math. 73 (1951), 368-380. (1951) MR0042005DOI10.2307/2372182
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.