Oscillation of nonlinear differential systems with retarded arguments期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Oscillation of nonlinear differential systems with retarded arguments

Authors:

Beatrix Ba?ová Bo?ena Dorociaková

Institution:

(1) Department of Mathematics, Faculty of Sciences, University of Zcaron

ilina, Slovak Republic;(2) Department of Applied Mathematics, Faculty of Mechanical Engineering, University of Zcaron

ilina, Slovak Republic

Abstract:

In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form

$y'_i \left( t \right) - p_i \left( t \right)y_{i + 1} \left( t \right) = 0,\quad i = 1,2,...,n - 2,$

$y'_{n - 1} \left( t \right) - p_{n - 1} \left( t \right)\left| {y_n \left( {h_n \left( t \right)} \right)^\alpha \operatorname{sgn} \left {y_n \left( {h_n \left( t \right)} \right)} \right]} \right| = 0,$

$y'_n \left( t \right)\operatorname{sgn} \left {y_1 \left( {h_1 \left( t \right)} \right)} \right] + p_n \left( t \right)\left| {y_1 \left( {h_1 \left( t \right)} \right)} \right|^\beta \leqslant 0,$

where n

3 is odd,

> 0,

> 0.This research was supported by the grants 1/8055/01 and 1/0026/03 of Scientific Grant Agency of Ministry of Education of Slovak Republic and Slovak Academy of Sciences.

Keywords:

nonlinear differential system oscillatory (nonoscillatory) solution

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