| Title:
|
Oscillation of nonlinear differential systems with retarded arguments (English) |
| Author:
|
Bačová, Beatrix |
| Author:
|
Dorociaková, Božena |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
255-262 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form \[ y^{\prime }_i(t)-p_i(t)y_{i+1}(t)=0, \quad i=1,2,\dots , n-2, y^{\prime }_{n-1}(t)-p_{n-1}(t)|y_n(h_n(t))|^\alpha \mathop {\mathrm sgn}[y_n(h_n(t))]=0, y^{\prime }_n(t) \mathop {\mathrm sgn}[y_1(h_1(t))]+p_n(t)|y_1(h_1(t))|^\beta \, \le 0, \] where $ n\ge 3 $ is odd, $ \alpha >0$, $ \beta >0$. (English) |
| Keyword:
|
nonlinear differential system |
| Keyword:
|
oscillatory (nonoscillatory) solution |
| MSC:
|
34K11 |
| MSC:
|
34K15 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1081.34080 |
| idMR:
|
MR2121671 |
| . |
| Date available:
|
2009-09-24T11:22:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127974 |
| . |
| Reference:
|
[1] R. G. Koplatadze and T. A. Chanturia: On the oscillatory and monotone solutions of the first order differential equations with deviating arguments.J. Diff. Equations 8 (1982), 1463–1465. (Russian) |
| Reference:
|
[2] I. Foltynska and J. Werbowski: On the oscillatory behaviour of solution of system of differential equation with deviating arguments.Colloquia Math. Soc. J. B., Qualitative theory of Diff. Eq. Szeged 30 (1979), 243–256. MR 0680596 |
| Reference:
|
[3] Y. Kitamura and T. Kusano: On the oscillation of a class of nonlinear differential systems with deviating argument.J. Math. Annal Appl. 66 (1978), 20–36. MR 0513483 |
| Reference:
|
[4] P. Marušiak: On the oscillation of nonlinear differential systems with retarded arguments.Math. Slovaca 34 (1984), 73–88. MR 0735938 |
| Reference:
|
[5] P. Marušiak and R. Olach: Functional Differential Equations.University of Žilina, EDIS, Žilina, 2000. (Slovak) |
| . |
