Boundedness of Solutions in Asymmetric Oscillations via the Twist Theorem

2001 ◽  
Vol 17 (2) ◽  
pp. 313-318
Author(s):  
Yi Qian Wang
Keyword(s):  
Boundedness Of Solutions ◽  
Twist Theorem ◽  
Asymmetric Oscillations

scholarly journals Boundedness of Solutions for a Class of Second-Order Periodic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Shunjun Jiang ◽  
Yan Ding
Keyword(s):  
Periodic Solutions ◽  
Periodic System ◽  
Second Order ◽  
Periodic Systems ◽  
Boundedness Of Solutions ◽  
Small Twist Theorem ◽  
Twist Theorem

In this paper we study the following second-order periodic system:x′′+V′(x)+p(x,t)=0,whereV(x)has a singularity. Under some assumptions on theV(x)andp(x,t)by Ortega’ small twist theorem, we obtain the existence of quasi-periodic solutions and boundedness of all the solutions.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

Sign in / Sign up

Export Citation Format

Share Document