scholarly journals Oscillation properties of nonlinear neutral differential equations ofnth order

2004 ◽  
Vol 2004 (71) ◽  
pp. 3893-3900
Author(s):  
T. Candan ◽  
R. S. Dahiya
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Asymptotic Properties ◽  
Neutral Functional Differential Equation ◽  
Neutral Differential Equations ◽  
Functional Differential ◽  
Oscillation Properties

We consider the nonlinear neutral functional differential equation[r(t)[x(t)+∫abp(t,μ)x(τ(t,μ))dμ](n−1)]′+δ∫cdq(t,ξ)f(x(σ(t,ξ)))dξ=0with continuous arguments. We will develop oscillatory and asymptotic properties of the solutions.

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 Asymptotic behaviour of solutions to neutral functional differential equations

1989 ◽  
Vol 40 (3) ◽  
pp. 345-355
Author(s):  
Shaozhu Chen ◽  
Qingguang Huang
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Functional Differential Equation ◽  
Necessary Conditions ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equation ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

Sufficient or necessary conditions are established so that the neutral functional differential equation [x(t) − G(t, xt)]″ + F(t, xt) = 0 has a solution which is asymptotic to a given solution of the related difference equation x(t) = G(t, xt) + a + bt, where a and b are constants.

Numerical Analysis of Fractional Neutral Functional Differential Equations Based on Generalized Volterra-Integral Operators

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
Xiao-Li Ding ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Differential Equations ◽  
Numerical Method ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Waveform Relaxation ◽  
Neutral Functional Differential Equation ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

We use waveform relaxation (WR) method to solve numerically fractional neutral functional differential equations and mainly consider the convergence of the numerical method with the help of a generalized Volterra-integral operator associated with the Mittag–Leffler function. We first give some properties of the integral operator. Using the proposed properties, we establish the convergence condition of the numerical method. Finally, we provide a new way to prove the convergence of waveform relaxation method for integer-order neutral functional differential equation, which is a special case of fractional neutral functional differential equation. Compared to the existing proof in the literature, our proof is concise and original.

scholarly journals Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Shurong Sun ◽  
Tongxing Li ◽  
Zhenlai Han ◽  
Yibing Sun
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equation ◽  
Neutral Functional Differential Equations ◽  
Mixed Nonlinearities ◽  
Functional Differential

We study the following second-order neutral functional differential equation with mixed nonlinearities(r(t)|(u(t)+p(t)u(t-σ))'|α-1(u(t)+p(t)u(t-σ))′)′+q0(t)|u(τ0(t))|α-1u(τ0(t))+q1(t)|u(τ1(t))|β-1u(τ1(t))+q2(t)|u(τ2(t))|γ-1u(τ2(t))=0, whereγ>α>β>0,∫t0∞(1/r1/α(t))dt<∞. Oscillation results for the equation are established which improve the results obtained by Sun and Meng (2006), Xu and Meng (2006), Sun and Meng (2009), and Han et al. (2010).

scholarly journals On the existence of positive solutions of a state-dependent neutral functional differential equation with two state-delay functions

2020 ◽  
Vol 4 (2) ◽  
pp. 132-141
Author(s):  
El-Sayed, A. M. A ◽  
◽  
Hamdallah, E. M. A ◽  
Ebead, H. R ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Positive Solutions ◽  
Functional Differential Equation ◽  
Continuous Dependence ◽  
Neutral Functional Differential Equation ◽  
Initial Value ◽  
State Delay ◽  
State Dependent ◽  
Existence Of Positive Solutions ◽  
Functional Differential

In this paper, we study the existence of positive solutions for an initial value problem of a state-dependent neutral functional differential equation with two state-delay functions. The continuous dependence of the unique solution will be proved. Some especial cases and examples will be given.

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