scholarly journals Existence of Almost Periodic Solutions to th-Order Neutral Differential Equations with Piecewise Constant Arguments

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rong-Kun Zhuang
Keyword(s):  
Positive Integer ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Neutral Differential Equations ◽  
Greatest Integer Function

We present some conditions for the existence and uniqueness of almost periodic solutions of th-order neutral differential equations with piecewise constant arguments of the form , here is the greatest integer function, and are nonzero constants, is a positive integer, and is almost periodic.

WEIGHTED PSEUDO ALMOST PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS

2015 ◽  
Vol 92 (2) ◽  
pp. 238-250 ◽  
Author(s):  
LI-LI ZHANG ◽  
HONG-XU LI
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Piecewise Constant Arguments ◽  
Periodic Sequences ◽  
Piecewise Constant ◽  
Pseudo Almost Periodic Solutions ◽  
Uniqueness Results ◽  
Pseudo Almost Periodic

By applying the theory of exponential dichotomies and contraction mapping, we establish some existence and uniqueness results for weighted pseudo almost periodic solutions of some differential equations with piecewise constant arguments. For this purpose, we also describe some basic properties of weighted pseudo almost periodic sequences.

scholarly journals Eberlein weak almost periodic solutions for a class of integro-differential equations with infinite delay

2018 ◽  
Vol 5 (1) ◽  
pp. 127-137
Author(s):  
Khalil Ezzinbi ◽  
Samir Fatajou ◽  
Fatima Zohra Elamrani
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Weakly Almost Periodic

AbstractIn thiswork,we provide sufficient conditions ensuring the existence and uniqueness of an Eberlein weakly almost periodic solutions for some semilinear integro-differential equations with infinite delay in Banach spaces. For illustration, we provide an example arising in viscoelasticity theory.

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