scholarly journals Almost periodic solutions of second order nonlinear differential equations with almost periodic forcing

1959 ◽  
Vol 10 (3) ◽  
pp. 425-425 ◽  
Author(s):  
C. E. Langenhop ◽  
G. Seifert
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Forcing

scholarly journals Periodic Properties of Solutions of Certain Second Order Nonlinear Differential Equations

2018 ◽  
Vol 10 (2) ◽  
pp. 29
Author(s):  
Akinwale Olutimo
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Basic Tool ◽  
Forcing Term ◽  
The Subject

Periodic properties of solutions play an important role in characterizing the behavior of solutions of sufficiently complicated nonlinear differential equations. Sufficient conditions are established which ensure the existence of periodic (or almost periodic) solutions of certain second nonlinear differential equations. Using the basic tool Lyapunov function, new result on the subject which improve some well known results in the literature with the particular cases of (1) for the existence of almost periodic or periodic solutions when the forcing term $p$ is almost periodic or periodic in t uniformly in $x$ and $\dot{x}$ are obtained. Our result further extends and improves on those that exist in the literature to the more general case considered.

Sign in / Sign up

Export Citation Format

Share Document