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《Journal of Shanghai Normal University(Natural Sciences)》 2011-01
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Running periodic solution of a class of second order differential equations

ZHAO Yan-ju,ZHOU Sheng-fan(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)  
We consider the second order differential equation with a damping coefficient: x″+ax′+g(x)=γ,this equation can model the motion of oscillators like the pendulum.First,we converse the second order differential equation to a equivalent system.After that,we prove this system exists the upper and lower solution.Finally,by the classical result of differential equation possesses running periodic solution,we prove that when g(x) is a segment linear function in a period,this system possesses a running periodic sultion,where this function includes two cases,symmetric and asymmetric in a period.This means the equivalent differential equation possesses a running periodic solution,and this solution has the nature of attracting other solutions.
【Fund】: 国家自然科学基金项目(11071165)
【CateGory Index】: O175.1
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