Oscillation of third-order nonlinear damped delay differential equations

Böhner, Martin; Grace, Said R.; Sağer, Ilgin; Tunç, Ercan

doi:10.1016/j.amc.2015.12.036

Cited by 37 publications

(38 citation statements)

References 16 publications

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“…Our aim here is to complement the work in [12], where the authors have shown by examples that the problem is open when n is odd. Moreover, we are able to extend and generalize some results obtained for third-order equations in [13]. The methods and arguments used in the present paper are different than the ones employed in [12].…”

Section: Introductionmentioning

confidence: 64%

“…It appears that the odd‐order case when is oscillatory is still open. In fact, a partial answer for n =3 has been given in in the sense that either is oscillatory or L 2 y ( t ) or L 1 y ( t ) is oscillatory. For instance, the equation

y^{'^{'}'} (t) + y^{'} (t) + \frac{2 ((), t^{3} + 2 t^{2} \sin (t) + 6 t - 12 \sin (t) + 9 t \cos (t))}{t^{3} (2 t - \sin (t))} y (t) = 0

has a nonoscillatory solution

y (t) = (2 t - \sin t) / t^{2}

satisfying but

L_{2} y = y^{'^{'}} (t)

is oscillatory.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, by Theorem and Theorem , we can replace condition by

λ \ln (\frac{1}{λ}) (\frac{1}{4} + \frac{a}{(n - 1)!}) > 1

and

a \ln (\frac{1}{λ}) > \frac{(n - 1)!}{e},

respectively. We should note that none of the results in can guarantee the oscillation of , even for the case n =3.…”

Section: Examplesmentioning

confidence: 95%

“…Notice that the structure of solutions may depend on the possibility of the function L n 1 y.t/ to be oscillatory, which was eliminated in [12,13] by imposing additional conditions. Because of the term L n 2 y.t/ in (1.2), the problem of nonexistence of a nonoscillatory solution y.t/ with y.t/L n 2 y.t/ < 0 seems to be crucial and challenging.…”

Section: Introductionmentioning

confidence: 99%

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Oscillation criteria for odd‐order nonlinear delay differential equations with a middle term

Grace

Jadlovská

Zafer

2017

Math Methods in App Sciences

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The oscillation of solutions of the nth‐order delay differential equation r2(t)r1(t)y(n−2)(t)α′′+p(t)y(n−2)(t)α+q(t)f(y(g(t)))=0 was studied in [S. R. Grace and A. Zafer, Math. Meth. Appl. Sci. 2016, 39 1150–1158] when n is even and the n odd case has been referred to as an interesting open problem. In the present work, our primary aim is to address this situation. Our method of the proof that is quite different from the aforementioned study is essentially new. We introduce Vn−1‐type solutions and use comparisons with first‐order oscillatory and second‐order nonoscillatory equations. Examples are given to illustrate the main results. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 64%

y^{'^{'}'} (t) + y^{'} (t) + \frac{2 ((), t^{3} + 2 t^{2} \sin (t) + 6 t - 12 \sin (t) + 9 t \cos (t))}{t^{3} (2 t - \sin (t))} y (t) = 0

has a nonoscillatory solution

y (t) = (2 t - \sin t) / t^{2}

satisfying but

L_{2} y = y^{'^{'}} (t)

is oscillatory.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, by Theorem and Theorem , we can replace condition by

λ \ln (\frac{1}{λ}) (\frac{1}{4} + \frac{a}{(n - 1)!}) > 1

and

a \ln (\frac{1}{λ}) > \frac{(n - 1)!}{e},

respectively. We should note that none of the results in can guarantee the oscillation of , even for the case n =3.…”

Section: Examplesmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Oscillation criteria for odd‐order nonlinear delay differential equations with a middle term

Grace

Jadlovská

Zafer

2017

Math Methods in App Sciences

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“…Bohner et al [6,7] and Džurina and Kotorová [10] studied the oscillatory behavior of a third-order delay differential equation with damping…”

Section: A(t) B(t) [X(t) + P(t)x(σ(t))]mentioning

confidence: 99%

Asymptotic behavior of third-order neutral differential equations with distributed deviating arguments

Wang¹,

Chen²,

Jiang³

et al. 2017

J. Math. Computer Sci.

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Oscillation theorems for fourth‐order delay differential equations with a negative middle term

Džurina

Jadlovská

2017

Math Methods in App Sciences

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This paper deals with the oscillation of the fourth-order linear delay differential equation with a negative middle term under the assumption that all solutions of the auxiliary third-order differential equation are nonoscillatory. Examples are included to illustrate the importance of results obtained. KEYWORDScomparison theorem, delay argument, fourth-order differential equations, oscillation y (4) (t) + q(t)y( (t)) = 0 7830

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Oscillation of third-order nonlinear damped delay differential equations

Cited by 37 publications

References 16 publications

Oscillation criteria for odd‐order nonlinear delay differential equations with a middle term

Oscillation criteria for odd‐order nonlinear delay differential equations with a middle term

Asymptotic behavior of third-order neutral differential equations with distributed deviating arguments

Oscillation theorems for fourth‐order delay differential equations with a negative middle term

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