Article
Full entry |
PDF
(1.5 MB)
Feedback
PDF
(1.5 MB)
Feedback
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; oscillatory solutions; nonoscillatory solutions
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.
References:
[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 10.32917/hmj/1206129616 | MR 0991245
[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 10.32917/hmj/1206135559 | MR 0466865
[4] P. Marušiak: Oscillation of solutions of nonlinear delay diffeгential equations. Mat. Čas. 4 (1974), 371-380. MR 0399620
[5] M. Švec: Suг un probléme aux limites. Czech. Mat. 5. 19 (1969), 17-26. MR 0237868
Search
Partner of
