| Title:
|
Asymptotic properties of solutions of functional differential systems (English) |
| Author:
|
Ivanov, Anatolij F. |
| Author:
|
Marušiak, Pavol |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
207-216 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper we study the existence of nonoscillatory solutions of the system $x^{(n)}_i(t)=\sum^2_{j=1}p_{ij}(t)f_{ij}(x_j(h_{ij}(t))), n\geq 2, i=1,2$, with the property $lim_{t\rightarrow \infty}x_i(t)/t^{k_i}=const \neq 0$ for some $k_i\in \{1,2,\ldots,n-1\}, i=1,2$. Sufficient conditions for the oscillation of solutions of the system are also proved. (English) |
| Keyword:
|
functional differential system |
| Keyword:
|
Schauder-Tichonov fixed point theorem |
| Keyword:
|
oscillatory and nonoscillatory solutions |
| Keyword:
|
prescribed asymptotics |
| Keyword:
|
oscillatory solutions |
| Keyword:
|
nonoscillatory solutions |
| MSC:
|
34C10 |
| MSC:
|
34K05 |
| MSC:
|
34K15 |
| MSC:
|
34K25 |
| MSC:
|
34K99 |
| idZBL:
|
Zbl 0757.34063 |
| idMR:
|
MR1165898 |
| DOI:
|
10.21136/MB.1992.125902 |
| . |
| Date available:
|
2009-09-24T20:52:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125902 |
| . |
| Reference:
|
[1] J. Jaroš T. Ҝusano: Oscillation theory of higheг order lineaг functional differential equations of natural type.Hirosh. Math. Ј. 18 (1988), 509-531. MR 0991245, 10.32917/hmj/1206129616 |
| Reference:
|
[2] I. T. Ҝiguradze: On the oscillation of solutions of the equation $d^m u / dt^m + a(t)|u|^n \sgn u = 0.Mat. Sb. 65 (1964), 172-187. (In Russian.) |
| Reference:
|
[3] Y. Ҝitamura: On nonoscialiatoгy solutions of functional differential equations with general deviating argument.Hirosh. Math. Ј. 8(1978), 49-62. MR 0466865, 10.32917/hmj/1206135559 |
| Reference:
|
[4] P. Marušiak: Oscillation of solutions of nonlinear delay diffeгential equations.Mat. Čas. 4 (1974), 371-380. MR 0399620 |
| Reference:
|
[5] M. Švec: Suг un probléme aux limites.Czech. Mat. 5. 19 (1969), 17-26. MR 0237868 |
| . |
