scholarly journals Asymptotic Properties of Solutions to Third-Order Nonlinear Neutral Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Qi Li ◽  
Rui Wang ◽  
Fanwei Meng ◽  
Jianxin Han
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Third Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

The aim of this work is to discuss asymptotic properties of a class of third-order nonlinear neutral functional differential equations. The results obtained extend and improve some related known results. Two examples are given to illustrate the main results.

scholarly journals Oscillation theorems of solution of second-order neutral differential equations

2021 ◽  
Vol 6 (11) ◽  
pp. 12771-12779
Author(s):  
Ali Muhib ◽  
◽  
Hammad Alotaibi ◽  
Omar Bazighifan ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Theoretical Support ◽  
Functional Differential ◽  
Oscillation Theorems ◽  
New Criteria ◽  
Oscillation Of Solutions

<abstract><p>In this paper, we aim to explore the oscillation of solutions for a class of second-order neutral functional differential equations. We propose new criteria to ensure that all obtained solutions are oscillatory. The obtained results can be used to develop and provide theoretical support for and further develop the oscillation study for a class of second-order neutral differential equations. Finally, an illustrated example is given to demonstrate the effectiveness of our new criteria.</p></abstract>

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

2012 ◽  
Vol 55 (4) ◽  
pp. 736-751 ◽  
Author(s):  
Eduardo Hernández ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Classical Solutions ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

AbstractIn this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

scholarly journals Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jin-Mun Jeong ◽  
Seong Ho Cho
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Functional Differential Equations ◽  
Fractional Power ◽  
Regularity Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied.

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

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