Differentiability of Solutions with Respect to the Initial Data in Differential Equations with State-dependent Delays

2011 ◽  
Vol 23 (4) ◽  
pp. 843-884 ◽  
Author(s):  
Ferenc Hartung
Keyword(s):  
Initial Data ◽  
Differential Equations ◽  
State Dependent ◽  
Differentiability Of Solutions

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.

scholarly journals Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

2020 ◽  
Vol 7 (1) ◽  
pp. 272-280
Author(s):  
Mamadou Abdoul Diop ◽  
Kora Hafiz Bete ◽  
Reine Kakpo ◽  
Carlos Ogouyandjou
Keyword(s):  
Differential Equations ◽  
Resolvent Operator ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Local Conditions ◽  
State Dependent ◽  
Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

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.

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