On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations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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On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations

Authors:

Institution:

(1) Department of Mathematics, Berhampur University, 760 007 Berhampur, India;(2) Department of Mathematics, Govt. Science College, 761 020 Chatrapur, India

Abstract:

In this paper, sufficient conditions have been obtained under which every solution of

$\left {y(t) \pm y(t - \tau )]'} \right. \pm Q(t)G(y(t - \sigma )) = f(t), t \geqslant 0$

, oscillates or tends to zero or to ±∞ → ∞. Usually these conditions are stronger than

$\int\limits_0^\infty {Q(t)dt = \infty }$

. An example is given to show that the condition (*) is not enough to arrive at the above conclusion. Existence of a positive (or negative) solution of

$y(t) - y(t - \tau )]' + Q(t)G(y(t - \sigma )) = f(t)$

is considered.

Keywords:

Oscillation nonoscillation neutral equations asymptotic behaviour

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