Oscillations of first-order neutral delay differential equations

Grammatikopoulos, M. K.; Grove, E.A.; Ladas, G.

doi:10.1016/0022-247x(86)90172-1

Cited by 65 publications

(40 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[10,11,12] PROOF. AS SF(0) = Q > 0 and Equation (2) has no real roots it follows that SF(X) > 0 for A e R. Also observe that dF(+<x>) = +oo.…”

Section: Preliminariesmentioning

confidence: 99%

“…Necessary and sufficient conditions (in terms of the characteristic equation) for the oscillation of all solutions of first order neutral differential equations have been obtained by Sficas and Stavroulakis [22], Grove, Ladas and Meimaridou [13], Kulenovic, Ladas and Meimaridou [16], Grammatikopoulos, Sficas and Stavroulakis [10], Farrell [7], and Grammatikopoulos and Stavroulakis [11,12]. Necessary and sufficient conditions for the oscillation of higher order equations have been obtained by Ladas, Sficas and Stavroulakis [18], Ladas, Partheniadis and Sficas [17], and Wang [25].…”

Section: D" [ (E 3 ) ^( 0 ŵmentioning

confidence: 99%

See 1 more Smart Citation

Oscillations of higher order neutral differential equations

1992

View full text Add to dashboard Cite

Consider the nth-order neutral differential equationwhere n> 1 , 8 = ± 1 , / , 31 are initial segments of natural numbers , p ( , T ; , a k 6 R and q k > 0 for i g / and k e 3T . Then a necessary and sufficient condition for the oscillation of all solutions of (E) is that its characteristic equation has no real roots. The method of proof has the advantage that it results in easily verifiable sufficient conditions (in terms of the coefficients and the arguments only) for the oscillation of all solutions of Equation (E).

show abstract

“…[10,11,12] PROOF. AS SF(0) = Q > 0 and Equation (2) has no real roots it follows that SF(X) > 0 for A e R. Also observe that dF(+<x>) = +oo.…”

Section: Preliminariesmentioning

confidence: 99%

Section: D" [ (E 3 ) ^( 0 ŵmentioning

confidence: 99%

Oscillations of higher order neutral differential equations

1992

View full text Add to dashboard Cite

show abstract

“…Integral conditions like (3) have been employed by many authors in the study of the oscillatory properties of various functional differential equations. For example, see papers by Grammatikopoulos, Grove and Ladas [7], by Ladas and Qian [11], and by Zhang and Gopalsamy [10].…”

Section: (T) + P(t)x(t − τ) = 0 (1)mentioning

confidence: 99%