scholarly journals Periodic solutions of differential equations with time lag containing a small parameter

1968 ◽  
Vol 4 (2) ◽  
pp. 160-175 ◽  
Author(s):  
Carlos Perelló
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Periodic Solutions ◽  
Time Lag

scholarly journals A New Approach to Approximate Solutions for Nonlinear Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Safia Meftah
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Small Parameter ◽  
Perturbation Method ◽  
Periodic Solutions ◽  
Asymptotic Expansions ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Approximation Methods ◽  
New Approach

The question discussed in this study concerns one of the most helpful approximation methods, namely, the expansion of a solution of a differential equation in a series in powers of a small parameter. We used the Lindstedt-Poincaré perturbation method to construct a solution closer to uniformly valid asymptotic expansions for periodic solutions of second-order nonlinear differential equations.

scholarly journals Periodic solutions of quasilinear non-autonomous systems with impulses

1985 ◽  
Vol 31 (2) ◽  
pp. 185-197 ◽  
Author(s):  
S.G. Hristova ◽  
D.D. Bainov
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Small Parameter ◽  
Periodic Solutions ◽  
Autonomous Systems ◽  
Sufficient Conditions ◽  
System Of Differential Equations ◽  
Image Position ◽  
The Given

The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the formwhere x ∈ Rn, ε is a small parameter,Sufficient conditions are found for the existence of the periodic solution of the given system in the critical and non-critical cases.

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