Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

Mathematica Slovaca

R. Rath¹  N. Misra¹  L. Padhy¹ 

关键词: neutral differential equation;    oscillation;    non-oscillation;   

DOI  :  10.2478/s12175-007-0006-7

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE) $$left[ {r(t)(y(t) - p(t)y(t - au ))'} ight]^prime + q(t)G(y(h(t))) = 0$$ are obtained, where q, h ∈ C([0, ∞), ℝ) such that q(t) ≥ 0, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C ([0, ∞), ℝ), G ∈ C (ℝ, ℝ) and τ ∈ ℝ+. Since the results of this paper hold when r(t) ≡ 1 and G(u) ≡ u, therefore it extends, generalizes and improves some known results.

【 授权许可】

Unknown