Article

 Title: Oscillatory properties of solutions of three-dimensional differential systems of neutral type (English) Author: Špániková, Eva Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 50 Issue: 4 Year: 2000 Pages: 879-887 Summary lang: English . Category: math . Summary: The purpose of this paper is to obtain oscillation criteria for the differential system \begin{aligned}{[y_1(t)-a(t)y_1(g(t))]}^{\prime}&=p_1(t)f_1(y_2(h_2(t))) \\ y_2^{\prime }(t)&=p_2(t)f_2(y_3(h_3(t))) \\ y_3^{\prime }(t)&= - p_3(t)f_3(y_1(h_1(t))), \quad t\in \mathbb R_+=[0,\infty ).\end{aligned} (English) Keyword: differential system of neutral type Keyword: oscillatory (nonoscillatory) solution MSC: 34K11 MSC: 34K15 MSC: 34K40 idZBL: Zbl 1079.34550 idMR: MR1792977 . Date available: 2009-09-24T10:38:47Z Last updated: 2016-04-07 Stable URL: http://hdl.handle.net/10338.dmlcz/127617 . Reference: [1] I. Foltynska and J. Werbowski: On the oscillatory behaviour of solutions of system of differential equations with deviating arguments.Colloq. Math. Soc. János Bolyai 30 (1979), Qualitative theory of Diff. Eq. Szegéd, 243–256. MR 0680596 Reference: [2] I. Györi and G. Ladas: Oscillation of systems of neutral differential equations.Differential Integral Equations 1 (1988), 281–286. MR 0929915 Reference: [3] A. F. Ivanov and P. Marušiak: Oscillatory properties of systems of neutral differential equations.Hiroshima Math. J. 24 (1994), 423–434. MR 1284384 Reference: [4] Y. Kitamura and T. Kusano: On the oscillation of a class of nonlinear differential systems with deviating argument.J. Math. Anal. Appl. 66 (1978), 20–36. MR 0513483, 10.1016/0022-247X(78)90267-6 Reference: [5] P. Marušiak: Oscillation criteria for nonlinear differential systems with general deviating arguments of mixed type.Hiroshima Math. J. 20 (1990), 197–208. MR 1050436 Reference: [6] P. Marušiak: Oscillatory properties of functional differential systems of neutral type.Czechoslovak Math. J. 43 (118) (1993), 649–662. MR 1258427 Reference: [7] B. Mihalíková: Some properties of differential systems with deviating arguments.Fasc. Math. 21 (1990), 5–26. MR 1115515 Reference: [8] V. Šeda: On nonlinear differential systems with deviating arguments.Czechoslovak Math. J. 36 (111) (1986), 450–466. MR 0847772 Reference: [9] V. N. Shevelo and V. N. Varech: On some properties of solutions of a system of functional differential equations.Kiev (1980), 153–171. (Russian) Reference: [10] V. N. Shevelo, V. N. Varech and A. G. Gritsai: Oscillations of components of solutions of systems of functional differential equations of neutral type.Inst. Mat. Preprint, Acad. Nauk Ukr. SSR. (1984), 116–126. (Russian) Reference: [11] E. Špániková: Asymptotic properties of solutions of nonlinear differential systems with deviating arguments.Čas. Pěst. Mat. (1990), no. 2, 178–191. Reference: [12] E. Špániková: Oscillatory properties of the solutions of three-dimensional nonlinear differential systems with deviating arguments.Acta Math. Univ. Comenian LIV–LV (1988), 173–183. MR 1083211 .

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