scholarly journals Lower Bounds of Periods of Periodic Solutions for a Class of Differential Equations with Variable Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Xin-Ge Liu ◽  
Mei-Lan Tang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Lower Bounds ◽  
Functional Differential Equations ◽  
Hölder Inequality ◽  
Simple Method ◽  
Variable Delays ◽  
Nonautonomous Differential Equations ◽  
Functional Differential ◽  
Wirtinger’S Inequality

Based on generalized Wirtinger's inequality, periods of periodic solutions of the nonautonomous differential equations with variable delays are investigated. Based on Hölder inequality, lower bounds of periods of periodic solutions for a class of functional differential equations with variable delays are obtained by a simple method.

scholarly journals Approximation methods and the generalised Fuller index for semi-flows in Banach spaces

1986 ◽  
Vol 29 (3) ◽  
pp. 299-308 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Functional Differential Equations ◽  
Periodic Points ◽  
Approximation Methods ◽  
Functional Differential ◽  
Linear Differential ◽  
Fuller Index

In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.

Sign in / Sign up

Export Citation Format

Share Document