Oscillation of Second-Order Neutral Differential Equations

Li, Tongxing; Rogovchenko, Yuri V.; Zhang, Chenghui

doi:10.1619/fesi.56.111

Cited by 56 publications

(53 citation statements)

References 11 publications

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“…As a matter of fact, ( E ) and its particular cases have numerous applications in physics and engineering; see, e.g., the papers by Agarwal et al. [2], Li and Rogovchenko [12–14], Wong [19], and Xu [22].…”

Section: Introductionmentioning

confidence: 99%

“…Most oscillation results given in the literature for ( E ) with a linear neutral term and its particular cases have been obtained under the assumption

A false(t_{0} false) : = \int_{t_{0}}^{\infty} \frac{1}{a^{1 / γ} false(t false)} d t = \infty,

which significantly simplifies the analysis of the behavior of

y false(t false) = x false(t false) + p false(t false) x^{α} false(τ (t) false)

for a nonoscillatory solution x of ( E ); see, e.g., the papers [13, 14, 21–23] and the references cited therein. In fact, if x is an eventually positive solution of ( E ), then

x (t) \geq (1 - p (t)) y (t)

holds assuming that

α = 1

, (1.1) (canonical case), and

0 \leq p (t) < 1

are satisfied.…”

Section: Introductionmentioning

confidence: 99%

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Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term

Džurina

Grace

Jadlovská

et al. 2020

Mathematische Nachrichten

Self Cite

139

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New oscillation criteria for the second-order Emden-Fowler delay differential equation with a sublinear neutral term are presented. An essential feature of our results is that oscillation of the studied equation is ensured via only one condition. Furthermore, as opposed to the results by Agarwal et al. criteria can be applied to Emden-Fowler delay differential equations with noncanonical operators and a sublinear neutral term. Our results essentially improve, extend, and simplify some known ones reported in the literature. The results are illustrated with examples. K E Y W O R D S delayed argument, Emden-Fowler differential equation, oscillation, second-order, sublinear neutral term M S C ( 2 0 1 0 ) 34C10, 34K11

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Section: Introductionmentioning

confidence: 99%

“…Most oscillation results given in the literature for ( E ) with a linear neutral term and its particular cases have been obtained under the assumption

A false(t_{0} false) : = \int_{t_{0}}^{\infty} \frac{1}{a^{1 / γ} false(t false)} d t = \infty,

which significantly simplifies the analysis of the behavior of

y false(t false) = x false(t false) + p false(t false) x^{α} false(τ (t) false)

for a nonoscillatory solution x of ( E ); see, e.g., the papers [13, 14, 21–23] and the references cited therein. In fact, if x is an eventually positive solution of ( E ), then

x (t) \geq (1 - p (t)) y (t)

holds assuming that

α = 1

, (1.1) (canonical case), and

0 \leq p (t) < 1

are satisfied.…”

Section: Introductionmentioning

confidence: 99%

Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term

Džurina

Grace

Jadlovská

et al. 2020

Mathematische Nachrichten

Self Cite

139

View full text Add to dashboard Cite

show abstract

“…The absolute majority of oscillation results in the literature concerns case (3), since in this case the positive solutions of (1) exhibit simpler behavior than in case (4); see Lemma 5 below. Case (4) has been studied, for example, in [9][10][11][12][13][14][15][16]. Note that for this case it is typical that the oscillation criterion consists of two relatively independent conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we essentially use the method from [1, 2] with a modification for case (4) presented in [12]. However, to keep the influence of each condition as transparent as possible we used different organization of the paper, as we explained above.…”

Section: Introductionmentioning

confidence: 99%

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On Eventually Positive Solutions of Quasilinear Second-Order Neutral Differential Equations

Fišnarová

Mařík

2014

Abstract and Applied Analysis

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We study the second-order neutral delay differential equation [ ( )Φ ( ( ))] + ( )Φ ( ( ( ))) = 0, where Φ ( ) = | | −1 , ≥ 1 and ( ) = ( ) + ( ) ( ( )). Based on the conversion into a certain first-order delay differential equation we provide sufficient conditions for nonexistence of eventually positive solutions of two different types. We cover both cases of convergent and divergent integral ∫ ∞ −1/ ( )d . A suitable combination of our results yields new oscillation criteria for this equation. Examples are shown to exhibit that our results improve related results published recently by several authors. The results are new even in the linear case.

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Forced oscillation of sublinear impulsive differential equations via nonprincipal solution

Naceri

Özbekler

2018

Math Methods in App Sciences

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MSC Classification: 34C10; 34C15 differential equations of the formwhere ∈ (0, 1), under the assumption that associated homogenous linear(ii) { i } is a strictly increasing unbounded sequence of real numbers, i ≥ t 0 and {q i } and { f i } are real sequences.Impulsive differential equations are of particular interest in many areas such as biology, physics, chemistry, control theory, and medicine as they model the real processes better than differential equations. Because of the lack of smoothness Math Meth Appl Sci. 2018;41:3335-3344.wileyonlinelibrary.com/journal/mma

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Oscillation of Second-Order Neutral Differential Equations

Cited by 56 publications

References 11 publications

Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term

Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term

On Eventually Positive Solutions of Quasilinear Second-Order Neutral Differential Equations

Forced oscillation of sublinear impulsive differential equations via nonprincipal solution

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