scholarly journals On the Asymptotic Periodic Solutions of Abstract Functional Differential Equations

2004 ◽  
Vol 47 (2) ◽  
pp. 307-327
Author(s):  
Takeshi Nishikawa ◽  
Nguyen Van Minh ◽  
Toshiki Naito
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Functional Differential

scholarly journals Approximation methods and the generalised Fuller index for semi-flows in Banach spaces

1986 ◽  
Vol 29 (3) ◽  
pp. 299-308 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Functional Differential Equations ◽  
Periodic Points ◽  
Approximation Methods ◽  
Functional Differential ◽  
Linear Differential ◽  
Fuller Index

In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.

scholarly journals Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Junwei Liu ◽  
Chuanyi Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Continuous Operator ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neutral Functional Differential Equations ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Exponentially Stable ◽  
Functional Differential

The existence of piecewise almost periodic solutions for impulsive neutral functional differential equations in Banach space is investigated. Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. An example is given to illustrate the theory.

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