scholarly journals Existence of Periodic Solutions for a Neutral Differential Equation with Piecewise Constant Argument

2005 ◽  
Vol 48 (2) ◽  
pp. 299-311 ◽  
Author(s):  
Gen-qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Neutral Differential Equation ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Existence Of Periodic Solutions ◽  
Constant Argument

scholarly journals Existence and Uniqueness of Periodic Solutions for a Second-Order Nonlinear Differential Equation with Piecewise Constant Argument

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Gen-qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Order Nonlinear Differential Equation ◽  
Constant Argument

Based on a continuation theorem of Mawhin, a unique periodic solution is found for a second-order nonlinear differential equation with piecewise constant argument.

scholarly journals Oscillatory and periodic solutions in alternately advanced and delayed differential equations

2013 ◽  
Vol 29 (2) ◽  
pp. 149-158
Author(s):  
KUO-SHOU CHIU ◽  
◽  
MANUEL PINTO ◽  
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Delayed Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Constant Argument

We examine scalar differential equations with a general piecewise constant argument (DEPCAG). It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without the argument deviations. Criteria for existence of periodic solutions of such equations are discussed.

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