Periodic solutions of neutral functional differential equations

1983 ◽  
pp. 115-121
Author(s):  
A. Cañada ◽  
P. Martinez-Amores
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

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.

scholarly journals Study of periodic and nonnegative periodic solutions of nonlinear neutral functional differential equations via fixed points

2016 ◽  
Vol 8 (2) ◽  
pp. 255-270
Author(s):  
Mouataz Billah Mesmouli ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
Completely Continuous ◽  
Continuous Map ◽  
Functional Differential ◽  
Large Contraction

Abstract In this paper, we study the existence of periodic and non-negative periodic solutions of the nonlinear neutral differential equation $${{\rm{d}} \over {{\rm{dt}}}}{\rm{x}}({\rm{t}}) = - {\rm{a}}\;({\rm{t}})\;{\rm{h}}\;({\rm{x}}\;({\rm{t}})) + {{\rm{d}} \over {{\rm{dt}}}}{\rm{Q}}\;({\rm{t}},\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))) + {\rm{G}}\;({\rm{t}},\;{\rm{x}}({\rm{t}}),\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))).$$ We invert this equation to construct a sum of a completely continuous map and a large contraction which is suitable for applying the modificatition of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions Q and G.

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