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 and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

2017 ◽  
Vol 25 (2) ◽  
pp. 89-98
Author(s):  
Gizem S. Oztepe ◽  
Fatma Karakoc ◽  
Huseyin Bereketoglu
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Second Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential ◽  
Constant Argument

Abstract This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.

Periodic solutions for a second-order differential equation with indefinite weak singularity

2019 ◽  
Vol 149 (5) ◽  
pp. 1135-1152 ◽  
Author(s):  
José Godoy ◽  
Manuel Zamora
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Second Order ◽  
Constant Sign ◽  
Piecewise Constant ◽  
Weak Singularity ◽  
Second Order Differential Equation ◽  
Image Position

AbstractAs a consequence of the main result of this paper efficient conditions guaranteeing the existence of a T −periodic solution to the second-order differential equation $${u}^{\prime \prime} = \displaystyle{{h(t)} \over {u^\lambda }}$$are established. Here, h ∈ L(ℝ/Tℤ) is a piecewise-constant sign-changing function and the non-linear term presents a weak singularity at 0 (i.e. λ ∈ (0, 1)).

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