Stability of State-Dependent Delay System

2013 ◽  
Author(s):  
Bin Li ◽  
Matthew Peet
Keyword(s):  
Delay System ◽  
State Dependent ◽  
State Dependent Delay

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.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

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