# Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments

Roman Koplatadze; N. L. Partsvania; Ioannis P. Stavroulakis

Archivum Mathematicum (2003)

- Volume: 039, Issue: 3, page 213-232
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topKoplatadze, Roman, Partsvania, N. L., and Stavroulakis, Ioannis P.. "Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments." Archivum Mathematicum 039.3 (2003): 213-232. <http://eudml.org/doc/249141>.

@article{Koplatadze2003,

abstract = {Sufficient conditions are established for the oscillation of proper solutions of the system \begin\{align\} u\_1^\{\prime \}(t) & =p(t)u\_2(\sigma (t))\,, \\ u\_2^\{\prime \}(t) & =-q(t)u\_1(\tau (t))\,, \end\{align\}
where $p,\,q: R_\{+\}\rightarrow R_\{+\}$ are locally summable functions, while $\tau $ and $\sigma : R_\{+\}\rightarrow R_\{+\}$ are continuous and continuously differentiable functions, respectively, and $\lim \limits _\{t\rightarrow +\infty \} \tau (t)=+\infty $, $\lim \limits _\{t\rightarrow +\infty \} \sigma (t)=+\infty $.},

author = {Koplatadze, Roman, Partsvania, N. L., Stavroulakis, Ioannis P.},

journal = {Archivum Mathematicum},

keywords = {two-dimensional differential system; proper solution; oscillatory system; two-dimensional differential system; proper solution; oscillatory system},

language = {eng},

number = {3},

pages = {213-232},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments},

url = {http://eudml.org/doc/249141},

volume = {039},

year = {2003},

}

TY - JOUR

AU - Koplatadze, Roman

AU - Partsvania, N. L.

AU - Stavroulakis, Ioannis P.

TI - Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments

JO - Archivum Mathematicum

PY - 2003

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 039

IS - 3

SP - 213

EP - 232

AB - Sufficient conditions are established for the oscillation of proper solutions of the system \begin{align} u_1^{\prime }(t) & =p(t)u_2(\sigma (t))\,, \\ u_2^{\prime }(t) & =-q(t)u_1(\tau (t))\,, \end{align}
where $p,\,q: R_{+}\rightarrow R_{+}$ are locally summable functions, while $\tau $ and $\sigma : R_{+}\rightarrow R_{+}$ are continuous and continuously differentiable functions, respectively, and $\lim \limits _{t\rightarrow +\infty } \tau (t)=+\infty $, $\lim \limits _{t\rightarrow +\infty } \sigma (t)=+\infty $.

LA - eng

KW - two-dimensional differential system; proper solution; oscillatory system; two-dimensional differential system; proper solution; oscillatory system

UR - http://eudml.org/doc/249141

ER -

## References

top- Chantladze T., Kandelaki N., Lomtatidze, A, Oscillation and nonoscillation criteria for a second order linear equation, Georgian Math. J. 6 (1999), No. 5, 401–414. (1999) Zbl0944.34025MR1692963
- Chantladze T., Kandelaki N., Lomtatidze A., On oscillation and nonoscillation of second order half-linear equation, Georgian Math. J. 7 (2000), No. 1, 329–346. MR1779555
- Coppell W. A., Stability and asymptotic behaviour of differential equations, Heat and Co., Boston, 1965. (1965)
- Hille E., Non-oscillation theorems, Trans. Amer. Math. Soc.64 (1948), 234–252. (1948) Zbl0031.35402MR0027925
- Koplatadze R. G., Criteria for the oscillation of solutions of second order differential inequalities and equations with a retarded argument, (Russian) Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 17 (1986), 104–121. (1986) MR0853276
- Koplatadze R., On oscillatory properties of solutions of functional differential equations, Mem. Differential Equations Math. Phys. 3 (1994), 1–179. (1994) Zbl0843.34070MR1375838
- Koplatadze R., Kvinikadze G., Stavroulakis I. P., Oscillation of second order linear delay differential equations, Funct. Differ. Equ. 7 (2000), No. 1–2, 121–145. Zbl1057.34077MR1941863
- Koplatadze R., Partsvania N., Oscillatory properties of solutions of two-dimensional differential systems with deviated arguments, (Russian) Differentsial’nye Uravneniya 33 (1997), No. 10, 1312–1320; translation in Differential Equations 33 (1997), No. 10, 1318–1326 (1998). (1997) MR1668129
- Lomtatidze A., Oscillation and nonoscillation criteria for second order linear differential equation, Georgian Math. J. 4 (1997), No. 2, 129–138. (1997) MR1439591
- Lomtatidze A., Partsvania N., Oscillation and nonoscillation criteria for two-dimensional systems of first order linear ordinary differential equations, Georgian Math. J. 6 (1999), No. 3, 285–298. (1999) Zbl0930.34025MR1679448
- Mirzov J. D., Asymptotic behavior of solutions of systems of nonlinear non-autonomous ordinary differential equations, (Russian) Maikop 1993. (1993)
- Nehari Z., Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428–445. (1957) Zbl0078.07602MR0087816
- Partsvania N., On oscillation of solutions of second order systems of deviated differential equations, Georgian Math. J. 3 (1996), No. 6, 571–582. (1996) Zbl0868.34054MR1419836

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.