On oscillation and asymptotic behaviour of a neutral differential equation of first order with positive and negative coefficients
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Date
2007-01-02
Authors
Rath, Radhanath
Mishra, Prayag Prasad
Padhi, Laxmi Narayan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper sufficient conditions are obtained so that every solution of
(y(t) - p(t)y(t - τ))′ + Q(t)G(y(t - σ)) - U(t)G(y(t - α)) = ƒ(t)
tends to zero or to ±∞ as t tends to ∞, where τ, σ, α are positive real numbers, p, ƒ ∈ C([0, ∞), R), Q, U ∈ C([0, ∞), [0, ∞)), and G ∈ C(R, R), G is non decreasing with xG(x) > 0 for x ≠ 0. The two primary assumptions in this paper ∫<sup>∞</sup><sub>t0</sub> Q(t) = ∞ and ∫∞t0 U(t) < ∞. The results hold when G is linear, super linear, or sublinear and also hold when ƒ(t) ≡ 0. This paper generalizes and improves some of the recent results in [5, 7, 8, 10].
Description
Keywords
Oscillatory solution, Nonoscillatory solution, Asymptotic behaviour
Citation
Rath, R., Mishra, P. P., & Padhy, L. N. (2007). On oscillation and asymptotic behaviour of a neutral differential equation of first order with positive and negative coefficients. <i>Electronic Journal of Differential Equations, 2007</i>(01), pp. 1-7.
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Attribution 4.0 International