# Asymptotic properties of solutions of functional differential systems

Mathematica Bohemica (1992)

• Volume: 117, Issue: 2, page 207-216
• ISSN: 0862-7959

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## Abstract

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In the paper we study the existence of nonoscillatory solutions of the system ${x}_{i}^{\left(n\right)}\left(t\right)={\sum }_{j=1}^{2}{p}_{ij}\left(t\right){f}_{ij}\left({x}_{j}\left({h}_{ij}\left(t\right)\right)\right),n\ge 2,i=1,2$, with the property $li{m}_{t\to \infty }{x}_{i}\left(t\right)/{t}^{{k}_{i}}=const\ne 0$ for some ${k}_{i}\in \left\{1,2,...,n-1\right\},i=1,2$. Sufficient conditions for the oscillation of solutions of the system are also proved.

## How to cite

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Ivanov, Anatolij F., and Marušiak, Pavol. "Asymptotic properties of solutions of functional differential systems." Mathematica Bohemica 117.2 (1992): 207-216. <http://eudml.org/doc/29056>.

@article{Ivanov1992,
abstract = {In the paper we study the existence of nonoscillatory solutions of the system $x^\{(n)\}_i(t)=\sum ^2_\{j=1\}p_\{ij\}(t)f_\{ij\}(x_j(h_\{ij\}(t))), n\ge 2, i=1,2$, with the property $lim_\{t\rightarrow \infty \}x_i(t)/t^\{k_i\}=const \ne 0$ for some $k_i\in \lbrace 1,2,\ldots ,n-1\rbrace , i=1,2$. Sufficient conditions for the oscillation of solutions of the system are also proved.},
author = {Ivanov, Anatolij F., Marušiak, Pavol},
journal = {Mathematica Bohemica},
keywords = {functional differential system; Schauder-Tichonov fixed point theorem; oscillatory and nonoscillatory solutions; prescribed asymptotics; oscillatory solutions; nonoscillatory solutions; functional differential system; Schauder-Tichonov fixed point theorem; oscillatory and nonoscillatory solutions; prescribed asymptotics},
language = {eng},
number = {2},
pages = {207-216},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic properties of solutions of functional differential systems},
url = {http://eudml.org/doc/29056},
volume = {117},
year = {1992},
}

TY - JOUR
AU - Ivanov, Anatolij F.
AU - Marušiak, Pavol
TI - Asymptotic properties of solutions of functional differential systems
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 2
SP - 207
EP - 216
AB - In the paper we study the existence of nonoscillatory solutions of the system $x^{(n)}_i(t)=\sum ^2_{j=1}p_{ij}(t)f_{ij}(x_j(h_{ij}(t))), n\ge 2, i=1,2$, with the property $lim_{t\rightarrow \infty }x_i(t)/t^{k_i}=const \ne 0$ for some $k_i\in \lbrace 1,2,\ldots ,n-1\rbrace , i=1,2$. Sufficient conditions for the oscillation of solutions of the system are also proved.
LA - eng
KW - functional differential system; Schauder-Tichonov fixed point theorem; oscillatory and nonoscillatory solutions; prescribed asymptotics; oscillatory solutions; nonoscillatory solutions; functional differential system; Schauder-Tichonov fixed point theorem; oscillatory and nonoscillatory solutions; prescribed asymptotics
UR - http://eudml.org/doc/29056
ER -

## References

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1. J. Jaroš T. Ҝusano, 10.32917/hmj/1206129616, Hirosh. Math. Ј. 18 (1988), 509-531. (1988) MR0991245DOI10.32917/hmj/1206129616
2. I. T. Ҝiguradze, [unknown], Mat. Sb. 65 (1964), 172-187. (In Russian.) (1964)
3. Y. Ҝitamura, 10.32917/hmj/1206135559, Hirosh. Math. Ј. 8(1978), 49-62. (1978) MR0466865DOI10.32917/hmj/1206135559
4. P. Marušiak, Oscillation of solutions of nonlinear delay diffeгential equations, Mat. Čas. 4 (1974), 371-380. (1974) MR0399620
5. M. Švec, Suг un probléme aux limites, Czech. Mat. 5. 19 (1969), 17-26. (1969) MR0237868

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