Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

Mathematica Slovaca

P. Mishra¹  R. Rath¹  N. Misra¹ 

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

DOI  :  10.2478/s12175-009-0140-5

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, sufficient conditions are obtained, so that the second order neutral delay differential equation $$(r(t)(y(t) - p(t)y(t - au ))')' + q(t)G(y(h(t)) = f(t)$$ has a positive and bounded solution, where q, h, f ∈ C ([0, ∞), ℝ) such that q(t) ≥ 0, but ≢ 0, h(t) ≤ t, h(t) → ∞ as t → ∞, r ∈ C (1) ([0, ∞), (0, ∞)), p ∈ C (2) [0, ∞), ℝ), G ∈ C(ℝ, ℝ) and τ ∈ ℝ+. In our work r(t) ≡ 1 is admissible and neither we assume G is non-decreasing, xG(x) > 0 for x ≠ 0, nor we take G is Lipschitzian. Hence the results of this paper improve many recent results.

【 授权许可】

Unknown