Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay

2018 ◽  
Vol 81 (1) ◽  
pp. 89-111 ◽  
Author(s):  
Eduardo Hernández ◽  
Jianhong Wu ◽  
Denis Fernandes
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Neutral Differential Equations ◽  
State Dependent ◽  
State Dependent Delay

scholarly journals An analysis on the stability of a state dependent delay differential equation

2016 ◽  
Vol 14 (1) ◽  
pp. 425-435 ◽  
Author(s):  
Sertaç Erman ◽  
Ali Demir
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Delay Term ◽  
State Dependent ◽  
State Dependent Delay ◽  
The Stability ◽  
Delay Differential ◽  
Equation With Delay

AbstractIn this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term $\tau (u(t)) = \frac{{a + bu(t)}}{{c + bu(t)}}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

A New Investigation on Fractional-Ordered Neutral Differential Systems with State-Dependent Delay

2019 ◽  
Vol 20 (7-8) ◽  
pp. 803-809 ◽  
Author(s):  
N. Valliammal ◽  
C. Ravichandran ◽  
Zakia Hammouch ◽  
Haci Mehmet Baskonus
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Existence Results ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Fractional Differential ◽  
Noncompact Measure ◽  
Equations With Delay

AbstractFractional differential equations with delay behaviors occur in fields like physical and biological ones with state-dependent delay or nonconstant delay and has drawn the attention of researchers. The main goal of the present work is to study the existence of mild solutions of neutral differential system along state-dependent delay in Banach space. By employing the fractional theory, noncompact measure and Mönch’s theorem, we investigate the existence results for neutral differential equations of fractional order with state-dependent delay. An illustration of derived results is offered.

-ASYMPTOTICALLY PERIODIC SOLUTIONS FOR ABSTRACT EQUATIONS WITH STATE-DEPENDENT DELAY

2018 ◽  
Vol 98 (3) ◽  
pp. 456-464 ◽  
Author(s):  
EDUARDO HERNÁNDEZ ◽  
MICHELLE PIERRI
Keyword(s):  
Population Dynamics ◽  
Differential Equations ◽  
Periodic Solutions ◽  
General Class ◽  
Existence And Uniqueness ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Asymptotically Periodic ◽  
Asymptotically Periodic Solutions

We study the existence and uniqueness of${\mathcal{S}}$-asymptotically periodic solutions for a general class of abstract differential equations with state-dependent delay. Some examples related to problems arising in population dynamics are presented.

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