| Title:
|
Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments (English) |
| Author:
|
Koplatadze, R. |
| Author:
|
Partsvania, N. L. |
| Author:
|
Stavroulakis, I. P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
213-232 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $. (English) |
| Keyword:
|
two-dimensional differential system |
| Keyword:
|
proper solution |
| Keyword:
|
oscillatory system |
| MSC:
|
34K06 |
| MSC:
|
34K11 |
| MSC:
|
34K25 |
| idZBL:
|
Zbl 1116.34331 |
| idMR:
|
MR2010723 |
| . |
| Date available:
|
2008-06-06T22:41:55Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107869 |
| . |
| Reference:
|
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| Reference:
|
[2] 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. MR 1779555 |
| Reference:
|
[3] Coppell W. A.: Stability and asymptotic behaviour of differential equations.Heat and Co., Boston, 1965. |
| Reference:
|
[4] Hille E.: Non-oscillation theorems.Trans. Amer. Math. Soc.64 (1948), 234–252. Zbl 0031.35402, MR 0027925 |
| Reference:
|
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| Reference:
|
[6] Koplatadze R.: On oscillatory properties of solutions of functional differential equations.Mem. Differential Equations Math. Phys. 3 (1994), 1–179. Zbl 0843.34070, MR 1375838 |
| Reference:
|
[7] 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. Zbl 1057.34077, MR 1941863 |
| Reference:
|
[8] 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). MR 1668129 |
| Reference:
|
[9] Lomtatidze A.: Oscillation and nonoscillation criteria for second order linear differential equation.Georgian Math. J. 4 (1997), No. 2, 129–138. MR 1439591 |
| Reference:
|
[10] 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. Zbl 0930.34025, MR 1679448 |
| Reference:
|
[11] Mirzov J. D.: Asymptotic behavior of solutions of systems of nonlinear non-autonomous ordinary differential equations.(Russian) Maikop 1993. |
| Reference:
|
[12] Nehari Z.: Oscillation criteria for second-order linear differential equations.Trans. Amer. Math. Soc. 85 (1957), 428–445. Zbl 0078.07602, MR 0087816 |
| Reference:
|
[13] Partsvania N.: On oscillation of solutions of second order systems of deviated differential equations.Georgian Math. J. 3 (1996), No. 6, 571–582. Zbl 0868.34054, MR 1419836 |
| . |
