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.

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.

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.

scholarly journals Qualitative Behaviors of Functional Differential Equations of Third Order with Multiple Deviating Arguments

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Third Order ◽  
Deviating Arguments ◽  
The Third ◽  
Multiple Deviating Arguments ◽  
Functional Differential ◽  
Made In

This paper considers nonautonomous functional differential equations of the third order with multiple constant deviating arguments. Using the Lyapunov-Krasovskii functional approach, we find certain sufficient conditions for the solutions to be stable and bounded. We give an example to illustrate the theoretical analysis made in this work and to show the effectiveness of the method utilized here.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

scholarly journals Oscillation Properties for Systems of Higher-Order Partial Differential Equations with Distributed Deviating Arguments

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Youjun Liu ◽  
Jianwen Zhang ◽  
Jurang Yan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Partial Differential ◽  
Deviating Arguments ◽  
Distributed Deviating Arguments ◽  
Functional Differential ◽  
Oscillation Properties

New sufficient conditions are obtained for oscillation for the solutions of systems of a class of higher-order quasilinear partial functional differential equations with distributed deviating arguments. The obtained results are illustrated by example.

scholarly journals An oscillation theorem for a superlinear functional differential equation with general deviating arguments

1978 ◽  
Vol 18 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Yuichi Kitamura ◽  
Takaŝsi Kusano
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Oscillation Criterion ◽  
Oscillation Theorem ◽  
Deviating Arguments ◽  
Fundamental Oscillation ◽  
Functional Differential ◽  
Image Position ◽  
Special Case ◽  
Fowler Equation

An oscillation criterion is established for a class of functional differential equations including the generalized Emden-Fowler equationas a special case. The deviating arguments involved may be retarded or advanced or otherwise. The result extends and improves known fundamental oscillation criteria for superlinear differential equations with retarded arguments.

scholarly journals OSCILLATION OF PARTIAL FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

1995 ◽  
Vol 26 (2) ◽  
pp. 131-139
Author(s):  
NORIO YOSHIDA
Keyword(s):  
Differential Equations ◽  
Parabolic Equations ◽  
Hyperbolic Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cylindrical Domain ◽  
Deviating Arguments ◽  
Partial Functional Differential Equations ◽  
All Solutions ◽  
Functional Differential

A class of partial functional-differential equations with deviating argu- ments including parabolic equations, hyperbolic equations and·beam equations is studied, and sufficient conditions are derived for all solutions of certain boundary value problem to be oscillatory in a cylindrical domain.

scholarly journals Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Cemil Tunç ◽  
Melek Gözen
Keyword(s):  
Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Functional Approach ◽  
Third Order ◽  
Deviating Arguments ◽  
The Third ◽  
Multiple Deviating Arguments ◽  
Functional Differential

We consider a nonautonomous functional differential equation of the third order with multiple deviating arguments. Using the Lyapunov-Krasovskiì functional approach, we give certain sufficient conditions to guarantee the asymptotic stability and uniform boundedness of the solutions.

scholarly journals Instability in Multi Delay Functional Differential Equations of Fourth Order

2015 ◽  
Vol 55 (1) ◽  
pp. 189-198
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Deviating Arguments ◽  
Multiple Deviating Arguments ◽  
The Subject ◽  
Functional Differential

AbstractA vector functional differential equation of the fourth order with multiple deviating arguments is considered. New sufficient conditions are established to guarantee the instability of the zero solution of the equation to be considered. We give an example to illustrate the subject.

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