# American Institute of Mathematical Sciences

March  2014, 13(2): 645-655. doi: 10.3934/cpaa.2014.13.645

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

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

Received  January 2013 Revised  July 2013 Published  October 2013

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 $p_i(t)\in C^5(R/Z).$
Citation: Daxiong Piao, Xiang Sun. Boundedness of solutions for a class of impact oscillators with time-denpendent polynomial potentials. Communications on Pure & Applied Analysis, 2014, 13 (2) : 645-655. doi: 10.3934/cpaa.2014.13.645
##### References:

show all references

##### References:
 [1] Yanmin Niu, Xiong Li. An application of Moser's twist theorem to superlinear impulsive differential equations. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 431-445. doi: 10.3934/dcds.2019017 [2] Huiping Jin. Boundedness in a class of duffing equations with oscillating potentials via the twist theorem. Communications on Pure & Applied Analysis, 2011, 10 (1) : 179-192. doi: 10.3934/cpaa.2011.10.179 [3] Holger Teismann. The Schrödinger equation with singular time-dependent potentials. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 705-722. doi: 10.3934/dcds.2000.6.705 [4] Nicola Guglielmi, László Hatvani. On small oscillations of mechanical systems with time-dependent kinetic and potential energy. Discrete & Continuous Dynamical Systems, 2008, 20 (4) : 911-926. doi: 10.3934/dcds.2008.20.911 [5] Božzidar Jovanović. Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems. Journal of Geometric Mechanics, 2018, 10 (2) : 173-187. doi: 10.3934/jgm.2018006 [6] Alessandro Fortunati, Stephen Wiggins. Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 1109-1118. doi: 10.3934/dcdss.2016044 [7] Florian Wagener. A parametrised version of Moser's modifying terms theorem. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 719-768. doi: 10.3934/dcdss.2010.3.719 [8] Yavar Kian, Alexander Tetlow. Hölder-stable recovery of time-dependent electromagnetic potentials appearing in a dynamical anisotropic Schrödinger equation. Inverse Problems & Imaging, 2020, 14 (5) : 819-839. doi: 10.3934/ipi.2020038 [9] Masahiro Ikeda, Ziheng Tu, Kyouhei Wakasa. Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021011 [10] Haixia Li. Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020088 [11] Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu. Periodic solutions for time-dependent subdifferential evolution inclusions. Evolution Equations & Control Theory, 2017, 6 (2) : 277-297. doi: 10.3934/eect.2017015 [12] Paul Deuring. Spatial asymptotics of mild solutions to the time-dependent Oseen system. Communications on Pure & Applied Analysis, 2021, 20 (5) : 1833-1849. doi: 10.3934/cpaa.2021044 [13] Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, 2021, 20 (3) : 995-1023. doi: 10.3934/cpaa.2021003 [14] Takeshi Fukao, Masahiro Kubo. Time-dependent obstacle problem in thermohydraulics. Conference Publications, 2009, 2009 (Special) : 240-249. doi: 10.3934/proc.2009.2009.240 [15] Giuseppe Maria Coclite, Mauro Garavello, Laura V. Spinolo. Optimal strategies for a time-dependent harvesting problem. Discrete & Continuous Dynamical Systems - S, 2018, 11 (5) : 865-900. doi: 10.3934/dcdss.2018053 [16] Francesco Di Plinio, Gregory S. Duane, Roger Temam. Time-dependent attractor for the Oscillon equation. Discrete & Continuous Dynamical Systems, 2011, 29 (1) : 141-167. doi: 10.3934/dcds.2011.29.141 [17] Morteza Fotouhi, Mohsen Yousefnezhad. Homogenization of a locally periodic time-dependent domain. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1669-1695. doi: 10.3934/cpaa.2020061 [18] G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini. Time-dependent systems of generalized Young measures. Networks & Heterogeneous Media, 2007, 2 (1) : 1-36. doi: 10.3934/nhm.2007.2.1 [19] Jin Takahashi, Eiji Yanagida. Time-dependent singularities in the heat equation. Communications on Pure & Applied Analysis, 2015, 14 (3) : 969-979. doi: 10.3934/cpaa.2015.14.969 [20] Hristo Genev, George Venkov. Soliton and blow-up solutions to the time-dependent Schrödinger-Hartree equation. Discrete & Continuous Dynamical Systems - S, 2012, 5 (5) : 903-923. doi: 10.3934/dcdss.2012.5.903

2020 Impact Factor: 1.916