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Boundedness of solutions for sublinear reversible systems

Authors:

LI Xiong

Institution:

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Abstract:

We are concerned with the boundedness of all the solutions for second order differential equation

$\ddot x + f\left( x \right)\dot x + g\left( x \right) = e\left( t \right),$

, wheref(x) andg(x) are odd, e( t) is odd and 1-periodic, andg(x) satisfies

$Sign \left( x \right) \cdot g\left( x \right) \to + \infty ,\frac{{g\left( x \right)}}{x} \to 0,as\left| x \right| \to + \infty .$

Keywords:

boundedness of solutions invariant tori reversible systems

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