scholarly journals On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Mukhiddin I Muminov
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Second Order ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Neutral Differential Equations

scholarly journals Existence conditions for periodic solutions of second-order neutral delay differential equations with piecewise constant arguments

2020 ◽  
Vol 18 (1) ◽  
pp. 93-105
Author(s):  
Mukhiddin I. Muminov ◽  
Ali H. M. Murid
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Second Order ◽  
Algebraic Equations ◽  
Neutral Delay ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Abstract In this paper, we describe a method to solve the problem of finding periodic solutions for second-order neutral delay-differential equations with piecewise constant arguments of the form x″(t) + px″(t − 1) = qx([t]) + f(t), where [⋅] denotes the greatest integer function, p and q are nonzero real or complex constants, and f(t) is complex valued periodic function. The method reduces the problem to a system of algebraic equations. We give explicit formula for the solutions of the equation. We also give counter examples to some previous findings concerning uniqueness of solution.

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.

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