scholarly journals Oscillatory Criteria for Higher Order Functional Differential Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Peiguang Wang ◽  
Hai Cai
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

We investigate a class of higher order functional differential equations with damping. By using a generalized Riccati transformation and integral averaging technique, some oscillation criteria for the differential equations are established.

scholarly journals New Oscillation Criteria for Third-Order Nonlinear Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Quanxin Zhang ◽  
Li Gao ◽  
Shouhua Liu ◽  
Yuanhong Yu
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper discusses oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, three new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve the earlier ones.

scholarly journals Oscillation criteria for half-linear function differential equations with damping

2014 ◽  
Vol 18 (5) ◽  
pp. 1537-1542 ◽  
Author(s):  
Jun Liu ◽  
Hong-Ying Luo ◽  
Xi Liu
Keyword(s):  
Differential Equations ◽  
Linear Function ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Functional Differential ◽  
Integral Average

In this paper, a class of half-linear functional differential equations with damping are studied. By using the generalized Riccati transformation and integral average skills, new oscillation criteria are obtained which generalize and improve some known results.

scholarly journals Oscillatory Properties of Solutions of Even-Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 212 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Rami Ahmad El-Nabulsi ◽  
Osama Moaaz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Even Order ◽  
Oscillatory Properties

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using Riccati transformation and the integral averaging technique, we obtain a new oscillation criteria. This new theorem complements and improves some known results from the literature. An example is provided to illustrate the main results.

scholarly journals Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yakun Wang ◽  
Fanwei Meng ◽  
Juan Gu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation

AbstractOur objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example to illustrate the main results.

scholarly journals On Delay-Independent Criteria for Oscillation of Higher-Order Functional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
Yuangong Sun
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Higher Order ◽  
Oscillation Criteria ◽  
Functional Differential ◽  
Delay Dependent

We investigate the oscillation of the following higher-order functional differential equation:x(n)(t)+q(t)|x(t-τ)|λ-1x(t-τ)=e(t),whereq(t)ande(t)are continuous functions on[t0,∞),1>λ>0andτ≠0are constants. Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the caseτ>0and the caseτ<0under the assumption that the potentialsq(t)ande(t)change signs on[t0,∞).

Oscillation Criterion of Third-Order Nonlinear Neutral Damped Functional Differential Equations

2012 ◽  
Vol 204-208 ◽  
pp. 4835-4839
Author(s):  
Yun Hui Zeng
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criterion ◽  
Third Order ◽  
Deviating Arguments ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Type Integral ◽  
Functional Differential

In this paper, A class of third-order nonlinear neutral damped functional differential equations with distributed deviating arguments are studied. By using a generalized Riccati transformation and Kamenev-type or Philos-type integral averaging technique,we establish some new sufficient conditions which insure that any solution of this equation oscillates or converges to zero.

Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Functional Differential Equations

2013 ◽  
Vol 303-306 ◽  
pp. 1247-1251
Author(s):  
Li Gao ◽  
Yuan Hong Yu ◽  
Quan Xin Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, two new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve earlier ones.

Oscillation of Second Order Half-Linear Differential Equations with Damping

2003 ◽  
Vol 10 (4) ◽  
pp. 785-797
Author(s):  
Qigui Yang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Linear Differential

Abstract This paper is concerned with a class of second order half-linear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing results.

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