On state-dependent delay partial neutral functional–differential equations

2007 ◽  
Vol 186 (1) ◽  
pp. 294-301 ◽  
Author(s):  
Eduardo Hernández M. ◽  
Mark A. McKibben
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential

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.

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.

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