scholarly journals Periodic Solutions of a Type of Liénard Higher Order Delay Functional Differential Equation with Complex Deviating Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Haiqing Wang
Keyword(s):  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Higher Order ◽  
Deviating Argument ◽  
Complex Deviating Argument ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

The author has studied the existence of periodic solutions of a type of higher order delay functional differential equations with neutral type by using the theory of coincidence degree, and some new sufficient conditions for the existence of periodic solutions have been obtained.

PERIODIC SOLUTIONS FOR SOME NONLINEAR PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

2010 ◽  
Vol 20 (02) ◽  
pp. 545-555 ◽  
Author(s):  
RACHID BENKHALTI ◽  
ABDELHAI ELAZZOUZI ◽  
KHALIL EZZINBI
Keyword(s):  
Periodic Solutions ◽  
Linear Part ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Functional Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Functional Differential ◽  
Partial Functional Differential Equation ◽  
Equation Of Neutral Type

In this work, we study the existence of periodic solutions for some nonlinear partial functional differential equation of neutral type. We assume that the linear part is nondensely defined and satisfies the Hille–Yosida condition. The delayed part is assumed to be ω-periodic with respect to the first argument. Using a fixed point theorem for multivalued mapping, some sufficient conditions are given to prove the existence of periodic solutions.

scholarly journals Periodic Solutions for a Class of -th Order Functional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Bing Song ◽  
Lijun Pan ◽  
Jinde Cao
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

We study the existence of periodic solutions forn-th order functional differential equations . Some new results on the existence of periodic solutions of the equations are obtained. Our approach is based on the coincidence degree theory of Mawhin.

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.

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

Periodic Solutions for a Class of Functional Differential Equations with State-Dependent Delay Close to Zero

2003 ◽  
Vol 13 (06) ◽  
pp. 807-841 ◽  
Author(s):  
R. Ouifki ◽  
M. L. Hbid
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Delay Equation ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

The purpose of the paper is to prove the existence of periodic solutions for a functional differential equation with state-dependent delay, of the type [Formula: see text] Transforming this equation into a perturbed constant delay equation and using the Hopf bifurcation result and the Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions for the state-dependent delay equation, bifurcating from r ≡ 0.

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