scholarly journals Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space

2016 ◽  
Vol 07 (15) ◽  
pp. 1726-1733 ◽  
Author(s):  
William Dimbour ◽  
Vincent Valmorin
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Nonlinear Differential Equation ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
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 Oscillation criteria for differential equations with piecewise constant argument

2001 ◽  
Vol 32 (4) ◽  
pp. 293-304
Author(s):  
Zhiguo Luo ◽  
Jianhua Shen
Keyword(s):  
Differential Equation ◽  
Continuous Functions ◽  
Variable Coefficients ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Greatest Integer Function ◽  
Special Case ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation ◽  
Constant Argument

We obtain some new oscillation and nonoscillation criteria for the differential equation with piecewise constant argument $$ x'(t) + a(t)x(t) + b(x) x([t-k]) = 0, $$ where $ a(t) $ and $ b(t) $ are continuous functions on $ [-k, \infty) $, $ b(t) \ge 0 $, $ k $ is a positive integer and $ [ \cdot ] $ denotes the greatest integer function. The method used is based on the treatment of certain difference equation with variable coefficients. Our results extend theorems in [15]. As a special case, our results also improve the conclusions obtained by Aftabizadeh, Wiener and Xu [3].

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