Boundedness of solutions for a class of impact oscillators with time-denpendent polynomial potentials

Daxiong Piao; Xiang Sun

doi:10.3934/cpaa.2014.13.645

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2014, Volume 13, Issue 2: 645-655. Doi: 10.3934/cpaa.2014.13.645

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Boundedness of solutions for a class of impact oscillators with time-denpendent polynomial potentials

Daxiong Piao^1, and
Xiang Sun^1,

1.
School of Mathematical Sciences, Ocean University of China, Qingdao 266100

Received: December 31, 2012

Revised: June 30, 2013

Published: February 2014

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Abstract

In this paper, we consider the boundedness of solutions for a class of impact oscillators with time dependent polynomial potentials, \begin{eqnarray} \ddot{x}+x^{2n+1}+\sum_{i=0}^{2n}p_{i}(t)x^{i}=0, \quad for\ x(t)> 0,\\ x(t)\geq 0,\\ \dot{x}(t_{0}^{+})=-\dot{x}(t_{0}^{-}), \quad if\ x(t_{0})=0, \end{eqnarray} where $n\in N^+$, $p_i(t+1)=p_i(t)$ and $p_i(t)\in C^5(R/Z).$

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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