Oscillation in First Order Neutral Differential Equations with "Integrally Small" Coefficients
نویسندگان
چکیده
منابع مشابه
Oscillation criteria for first-order neutral differential equations
d Ž . Ž . Ž . Sufficient conditions for the oscillation of the equation x t R t x t r dt Ž . Ž . Ž . Ž . Ž . . Ž . P t x t Q t x t 0, where P, Q, R C t , , R , r 0, , 0 Ž . t Ž . , R , , are obtained where R t H Q u du 1 is allowed to t Ž . Ž . Ž . Ž oscillate and the condition H s P s Q s H P u Q u t s 0 . du ds is not necessary. Some examples are given, which show that the results here are al...
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In this paper, we shall consider higher order nonlinear neutral delay differential equation of the type [x(t) + p(t)x(τ(t))] + q(t) [x(σ(t))] = 0, t ≥ t0, n ∈ N, (*) where p ∈ C ([t0,∞) ,R) is oscillatory and lim t→∞ p(t) = 0, q ∈ C ( [t0,∞) ,R ) , τ, σ ∈ C ([t0,∞) ,R), τ(t), σ(t) < t, lim t→∞ τ(t) = lim t→∞ σ(t) =∞ and α ∈ (0,∞) is a ratio of odd positive integers. If α ∈ (0, 1), equation (*) ...
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and Applied Analysis 3 By using weaker conditions than in 4, 10 , Karpuz et al. 1 have established oscillation criteria for differential equation [ x t ∑ i∈R ri t x αi t ]′′ ∑ i∈P pi t x ( βi t ) − ∑ i∈Q qi t x ( γi t ) f t . 1.6 In this paper, we shall continue in the direction to study the oscillatory properties of 1.1 and 1.2 . We establish new oscillation criteria for 1.1 and 1.2 , which ex...
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By a solution to (.), we mean a function x ∈ C([Tx,∞),R), Tx ≥ t which has the property r(z′)α ∈ C([Tx,∞),R) and satisfies (.) on the interval [Tx,∞). We consider only those solutions of (.) which satisfy condition sup{|x(t)| : t ≥ T} > for all T ≥ Tx and assume that (.) possesses such solutions. As usual, a solution of (.) is called oscillatory if it has arbitrarily large zeros o...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1994
ISSN: 0022-247X
DOI: 10.1006/jmaa.1994.1362