scholarly journals On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses

Cubo (Temuco) ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 61-75 ◽  
Author(s):  
Khalida Aissani ◽  
Mouffak Benchohra ◽  
Nadia Benkhettou
Keyword(s):  
Differential Equations ◽  
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 On time transformations for differential equations with state-dependent delay

2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Alexander Rezounenko
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
The State ◽  
Delay Systems ◽  
Constant Delay ◽  
Systems Of Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Time Transformations

AbstractSystems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.

Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay

2019 ◽  
Vol 62 (3) ◽  
pp. 771-788 ◽  
Author(s):  
Eduardo Hernández ◽  
Jianhong Wu
Keyword(s):  
Population Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Solutions ◽  
Almost Periodic ◽  
Qualitative Properties ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Asymptotically Almost Periodic

AbstractWe study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.

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