scholarly journals Periodic solutions of a class of hyperbolic equations containing a small parameter

1967 ◽  
Vol 23 (5) ◽  
pp. 380-398 ◽  
Author(s):  
Jack K. Hale
Keyword(s):  
Small Parameter ◽  
Periodic Solutions ◽  
Hyperbolic Equations

Time-periodic solutions of symmetric hyperbolic systems

2020 ◽  
Vol 17 (04) ◽  
pp. 707-726
Author(s):  
Masashi Ohnawa ◽  
Masahiro Suzuki
Keyword(s):  
Periodic Solutions ◽  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Unique Existence ◽  
Periodic Problems ◽  
Time Periodic Solutions ◽  
External Forces ◽  
Initial Boundary Value ◽  
Time Periodic

We prove the unique existence of time-periodic solutions to general hyperbolic equations with periodic external forces autonomous or nonautonomous over a domain bounded by two parallel planes, provided that all the characteristics with respect to the direction normal to the planes have the same sign. It is also shown that global-in-time solutions to initial-boundary value problems coincide with the solutions to corresponding time-periodic problems after a finite time. We devote one section to the reformulation of several realistic problems and see our results have wide applicability.

Complicated Bifurcations of Periodic Solutions in Some System of Ode

1996 ◽  
Vol 39 (3) ◽  
pp. 360-366 ◽  
Author(s):  
A. Soleev
Keyword(s):  
Small Parameter ◽  
Periodic Solutions ◽  
Stationary Solution ◽  
Real Analytic ◽  
Order Four

AbstractIn a vicinity of a stationary solution we consider a real analytic system of ODE of order four, depending on a small parameter. We look for families of periodic solutions which contract to the stationary solution, when the parameter tends to zero. We apply the general methods developed in [2] for the study of complex bifurcations and in [4] for local resolutions of singularities.

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.

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