Oscillation of First Order Neutral Delay Differential Equations
نویسندگان
چکیده
منابع مشابه
Oscillation of Nonlinear Neutral Delay Differential Equations of Second Order
Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...
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We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations.We study the case of superlinear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate th...
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Neutral differential equations find numerous applications in natural science and technology. For instance, they are frequently used for the study of distributed networks containing lossless transmission lines; see Hale 1 . In recent years, many studies have been made on the oscillatory behavior of solutions of neutral delay differential equations, and we refer to the recent papers 2–23 and the ...
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and Applied Analysis 3 Theorem 2.1. Assume that 1.4 holds, 0 ≤ p t ≤ p1 < 1. If for some function ρ ∈ C1 t0,∞ , 0,∞ , for all sufficiently large t1 ≥ t0 and for t3 > t2 > t1, one has lim sup t→∞ ∫ t t3 ⎛ ⎜⎝ρ s q s (1 − p τ s ) ∫τ s t2 (∫v t1 1/a u du/b v ) dv ∫s t1 1/a u du − a s ( ρ′ s )2 4ρ s ⎞ ⎟⎠ds ∞, 2.1 ∫∞
متن کاملOscillation of Second Order Neutral Delay Differential Equations
We present new oscillation criteria for the second order nonlinear neutral delay differential equation ( a (t) (y (t)+ p (t) y (t − τ))′)′ + q (t) |y (σ (t))|α−1 y (σ (t)) = 0, where t ≥ t0, τ, and α are positive constants and the functions p, q, a, σ ∈ C ([t0,∞) ,R) . Our results generalize and improve some known results for oscillation of second order neutral delay differential equations. Our...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1995
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1444