Geodesic
Asymptotic properties of solutions of functional differential systems
Mathematica Bohemica, Tome 117 (1992) no. 2, pp. 207-216

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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.
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.
DOI : 10.21136/MB.1992.125902
Classification : 34C10, 34K05, 34K15, 34K25, 34K99
Keywords: functional differential system; Schauder-Tichonov fixed point theorem; oscillatory and nonoscillatory solutions; prescribed asymptotics; oscillatory solutions; nonoscillatory solutions 
Ivanov, Anatolij F.; Marušiak, Pavol. Asymptotic properties of solutions of functional differential systems. Mathematica Bohemica, Tome 117 (1992) no. 2, pp. 207-216. doi: 10.21136/MB.1992.125902
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[1] J. Jaroš T. Ҝusano: Oscillation theory of higheг order lineaг functional differential equations of natural type. Hirosh. Math. Ј. 18 (1988), 509-531. | DOI | MR

[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.)

[3] Y. Ҝitamura: On nonoscialiatoгy solutions of functional differential equations with general deviating argument. Hirosh. Math. Ј. 8(1978), 49-62. | DOI | MR

[4] P. Marušiak: Oscillation of solutions of nonlinear delay diffeгential equations. Mat. Čas. 4 (1974), 371-380. | MR

[5] M. Švec: Suг un probléme aux limites. Czech. Mat. 5. 19 (1969), 17-26. | MR

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