Mild solutions for impulsive neutral functional differential equations with state-dependent delay

2010 ◽  
Vol 80 (3) ◽  
pp. 375-390 ◽  
Author(s):  
Claudio Cuevas ◽  
Gaston M. N’Guérékata ◽  
Marcos Rabelo
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential

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.

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.

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