Integral Oscillation Criteria for Third-Order Differential Equations With Delay Argument

Džurina, Jozef; Baculíková, Blanka; Jadlovská, Irena

doi:10.12732/ijpam.v108i1.15

Cited by 4 publications

(1 citation statement)

References 13 publications

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“…We first present the following classes of nonoscillatory (let us say positive) solutions of (1.1): z(t) ∈ N I ⇔ z (t) > 0, z (t) > 0, (r(t)(z (t)) α ) < 0, z(t) ∈ N II ⇔ z (t) < 0, z (t) > 0, (r(t)(z (t)) α ) < 0, and z(t) ∈ N III ⇔ z (t) > 0, z (t) < 0, (r(t)(z (t)) α ) < 0, eventually. The following lemma comes directly from combining Lemma 1 and Lemma 2 in [13] with Lemma 3 and Lemma 4 in [20]. Proof See [21, p. 28].…”

Section: Some Preliminariesmentioning

confidence: 99%

Oscillation of solutions of third order nonlinear neutral differential equations

2020

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The main objective of this article is to improve and complement some of the oscillation criteria published recently in the literature for third order differential equation of the form (r(t)(z (t)) α) + q(t)f (x(σ (t))) = 0, t ≥ t 0 > 0, where z(t) = x(t) + p(t)x(τ (t)) and α is a ratio of odd positive integers in the two cases ∞ t 0 r-1 α (s) ds < ∞ and ∞ t 0 r-1 α (s) ds = ∞. Some illustrative examples are presented.

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Section: Some Preliminariesmentioning

confidence: 99%

Oscillation of solutions of third order nonlinear neutral differential equations

2020

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Oscillation of nonlinear third-order differential equations with several sublinear neutral terms

El-Sheikh

Sallam

Salem

2021

Mathematica Slovaca

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A class of third order differential equations with several sublinear neutral terms of the type ( a ( t ) ( b ( t ) ( x ( t ) + ∑ j = 1 n p j ( t ) x α j ( τ j ( t ) ) ) ′ ) ′ ) ′ + ∑ i = 1 m f i ( t , x ( σ i ( t ) ) ) = 0 , t ≥ t 0 > 0 $$\begin{array}{} \displaystyle \bigg( a(t)\Big( b(t)\Big(x(t)+\sum\limits_{j=1}^{n}p_{j}(t)x^{\alpha _{j}}(\tau _{j}(t))\Big)'\Big)'\bigg)' +\sum\limits_{i=1}^{m}f_{i}(t,x(\sigma _{i}(t)))=0,\qquad t\geq t_{0} \gt 0 \end{array}$$ is considered. Some oscillation criteria are presented to improve and complement those in the literature. Two examples are established to illustrate the main results.

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Property $ \bar{A} $ of third-order noncanonical functional differential equations with positive and negative terms

Sangeetha

Thamilvanan

Santra

et al. 2023

MATH

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<abstract>In this article, we have derived a new method to study the oscillatory and asymptotic properties for third-order noncanonical functional differential equations with both positive and negative terms of the form <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} (p_2 (t)(p_1 (t) x'(t) )')'+a(t)g(x(\tau(t)))-b(t)h(x(\sigma(t)) = 0 \end{equation*} $\end{document} </tex-math></disp-formula> Firstly, we have converted the above equation of noncanonical type into the canonical type using the strongly noncanonical operator and obtained some new conditions for Property $ \bar{A} $. We furnished illustrative examples to validate our main result.</abstract>

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Integral Oscillation Criteria for Third-Order Differential Equations With Delay Argument

Abstract: In the present paper, some new criteria for property A and the oscillation of third order nonlinear delay differential equations of the typeare established.

Cited by 4 publications

References 13 publications

Oscillation of solutions of third order nonlinear neutral differential equations

Oscillation of solutions of third order nonlinear neutral differential equations

Oscillation of nonlinear third-order differential equations with several sublinear neutral terms

Property $ \bar{A} $ of third-order noncanonical functional differential equations with positive and negative terms

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