scholarly journals Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
B. Baculíková
Keyword(s):  
Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Comparison Theorems ◽  
Third Order ◽  
Nonlinear Functional ◽  
The Third ◽  
Property B ◽  
Functional Differential ◽  
Mixed Arguments

The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments . Both cases and are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

scholarly journals On Properties of Third-Order Differential Equations via Comparison Principles

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
B. Baculíková ◽  
J. Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Canonical Form ◽  
Functional Differential Equation ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Comparison Theorems ◽  
Third Order ◽  
The Third ◽  
Functional Differential

The objective of this paper is to offer sufficient conditions for certain asymptotic properties of the third-order functional differential equation , where studied equation is in a canonical form, that is, . Employing Trench theory of canonical operators, we deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

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.

Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

2012 ◽  
Vol 616-618 ◽  
pp. 2137-2141
Author(s):  
Zhi Min Luo ◽  
Bei Fei Chen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Nonlinear Functional Differential Equation ◽  
Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

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 Asymptotic behavior of nonoscillatory solutions of a higher order functional differential equation

1981 ◽  
Vol 24 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Approach Zero ◽  
Image Position

The asymptotic behavior of nonoscillatory solutions of nth order nonlinear functional differential equationsis investigated. Sufficient conditions are provided which ensure that all nonoscillatory solutions approach zero as t → ∞.

scholarly journals Nonoscillation theorems for functional differential equations of arbitrary order

1984 ◽  
Vol 7 (2) ◽  
pp. 249-256 ◽  
Author(s):  
John R. Graef ◽  
Myron K. Grammatikopoulos ◽  
Yuichi Kitamura ◽  
Takasi Kusano ◽  
Hiroshi Onose ◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Arbitrary Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Nonoscillation Theorem

The authors give sufficient conditions for all oscillatory solutions of a sublinear forced higher order nonlinear functional differential equation to converge to zero. They then prove a nonoscillation theorem for such equations. A few intermediate results are also obtained.

scholarly journals A nonoscillation theorem for a second order sublinear retarded differential equation

1976 ◽  
Vol 15 (3) ◽  
pp. 401-406 ◽  
Author(s):  
Takaŝi Kusano ◽  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Functional ◽  
Retarded Differential Equation ◽  
All Solutions ◽  
Functional Differential ◽  
Nonoscillation Theorem

Sufficient conditions are obtained for all solutions of a class of second order nonlinear functional differential equations to be nonoscillatory.

scholarly journals Asymptotic Properties of Third-Order Nonlinear Differential Equations

2013 ◽  
Vol 54 (1) ◽  
pp. 19-29
Author(s):  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Comparison Theorems ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Advanced Case ◽  
The Third ◽  
Functional Differential ◽  
New Criteria

Abstract We present new criteria guaranteeing that all nonoscillatory solutions of the third-order functional differential equation tend to zero. Our results are based on the suitable comparison theorems. We consider both delay and advanced case of studied equation. The results obtained essentially improve and complement 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.

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