Abstract
Consider the neutral delay differential equation urn:x-wiley:01611712:media:ijmm295109:ijmm295109-math-0001 Where P, Q?C([t0, 8], R+), t?(0, 8) and d?R+. We obtain several sufficient conditions for the oscillation of all solutions of Eq. (*) without the restriction urn:x-wiley:01611712:media:ijmm295109:ijmm295109-math-0002
Highlights
In this paper we consider the first order neutral delay differential equation d[x(t) dt+ P(t)x(t r)] Q(t)x(t a) 0 t to (I)where r (O,oo),a R+ and P,Q C([to,OO),R+) (2)Our aim in this paper is to establish some sufficient conditions for the oscillation of all solutions of Eq (1) which does not require thatThe oscillatory behavior of Eq (1) has been investigated by many authors,see for example[-1--2] and [-4--7]
The main results are Lemmas 1 and 2 which enable us to establish some new type of oscillation criteria for Eq (1)
By using induction,we can get,for some sufficiently large tt+z, y’ (t) 2+Mr+tQ(t)H(t),for t t+z which,together with (Yz),yields y(t) oo as t which contradicts the hypothesis that y (t) is eventually positive
Summary
In this paper we consider the first order neutral delay differential equation d[x(t) dt+ P(t)x(t r)] Q(t)x(t a) 0 t to (I)where r (O,oo),a R+ and P,Q C([to,OO),R+) (2)Our aim in this paper is to establish some sufficient conditions for the oscillation of all solutions of Eq (1) which does not require thatThe oscillatory behavior of Eq (1) has been investigated by many authors,see for example[-1--2] and [-4--7]. We obtain several sufficient conditions for the oscillation of all solutions of Eq (*) without the restriction Our aim in this paper is to establish some sufficient conditions for the oscillation of all solutions of Eq (1) which does not require that Every bounded solution of Eq (1)oscillates if and only if
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