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.

Topological transversality and periodic solutions of neutral functional differential equations

1999 ◽  
Vol 129 (1) ◽  
pp. 199-220 ◽  
Author(s):  
Jianhong Wu ◽  
Huaxing Xia ◽  
Bo Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
A Priori ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
General Existence ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

In this paper, we study the existence of periodic solutions of neutral functional differential equations (NFDEs). A topological transversality theorem is used to obtain fixed points of certain nonlinear compact operators, which correspond to periodic solutions of the original differential equations. The method relies on a priori bounds on periodic solutions to a family of appropriately constructed NFDEs. A general existence theorem is proved and several illustrative examples are given where we use Liapunov-like functions in deriving such a priori bounds on periodic solutions. Due to the topological nature of the approach, the theorem applies as well to NFDEs of mixed type and NFDEs with state-dependent delay. Some comparisons between our results and the existing ones are also provided.

On the existence of periodic solutions for autonomous retarded functional differential equations on R2

1986 ◽  
Vol 102 (3-4) ◽  
pp. 259-262 ◽  
Author(s):  
J. G. Dos Reis ◽  
R. L. S. Baroni
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Retarded Functional Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

scholarly journals Global Existence for Functional Differential Equations with State-Dependent Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mouffak Benchohra ◽  
Imene Medjadj ◽  
Juan J. Nieto ◽  
P. Prakash
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential

Our aim in this work is to study the existence of solutions of a functional differential equation with state-dependent delay. We use Schauder's fixed point theorem to show the existence of solutions.

scholarly journals Existence of Periodic Solutions to Multidelay Functional Differential Equations of Second Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Ramazan Yazgan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Functional Approach ◽  
Second Order ◽  
Nonlinear Functional ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

Using Lyapunov-Krasovskii functional approach, we establish a new result to guarantee the existence of periodic solutions of a certain multidelay nonlinear functional differential equation of second order. By this work, we extend and improve some earlier result in the literature.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

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