scholarly journals Collocation schemes for periodic solutions of neutral delay differential equations

2006 ◽  
Vol 12 (11) ◽  
pp. 1087-1101 ◽  
Author(s):  
David A. W. Barton ◽  
Bernd KrauskopF ◽  
R. Eddie Wilson
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

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 Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

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