Abstract
Abstract This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equations ( r ( t ) [ x ( t ) + p ( t ) x ( τ ( t ) ) ] Δ ) Δ + q ( t ) x ( δ ( t ) ) = 0 , on a time scale T with sup T = ∞ , where 0 ≤ p ( t ) ≤ p 0 < ∞ . Some new results are presented that not only complement and improve those related results in the literature, but also improve some known results for a second-order delay dynamic equation without a neutral term. Further, the main results improve some related results for second-order neutral differential equations. MSC:34K11, 34N05, 39A10.
Highlights
1 Introduction In this paper, we are concerned with oscillation of a class of second-order neutral delay dynamic equations, r(t) x(t) + p(t)x τ (t)
There has been an increasing interest in obtaining sufficient conditions for oscillatory or nonoscillatory behavior of different classes of differential equations and dynamic equations on time scales; we refer the reader to the papers [ – ]
For oscillation of second-order dynamic equations on time scales, Erbe et al [ ] established a sufficient condition which ensures that the solution x of the delay dynamic equation r(t)x (t) + q(t)x τ (t) =
Summary
There has been an increasing interest in obtaining sufficient conditions for oscillatory or nonoscillatory behavior of different classes of differential equations and dynamic equations on time scales; we refer the reader to the papers [ – ]. Regarding oscillation of second-order neutral differential equations, Grammatikopoulos et al [ ] established that the condition q(s) – p(s – δ) ds = ∞
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