| 具有障碍的二阶Hamilton系统的周期解 |
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| 引用本文： | 王少敏,熊明.具有障碍的二阶Hamilton系统的周期解[J].湖南理工学院学报,2012(1):12-15,56. |
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| 作者姓名： | 王少敏 熊明 |
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| 作者单位： | 大理学院数学与计算机学院 |
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| 基金项目： | 国家自然科学基金项目(10561011);云南省教育厅科学研究基金项目(09Y0367) |
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| 摘 要： | 二阶Hamilton系统:-=f(t,x)满足初始条件x(t)≥0,t∈R,且当x(t0)=0时,(t0-)=(t0+)=,在一定条件下,等价于系统{-=f(t,|x|)sgn(x),x(0)-x(2π)=(0)-(2π)=0{-=f(t,|x|)sgn(x),x(0)-x(2π)=(0)-(2π)=0本文使用非光滑情形下的一个新临界点定理得到系统(Ⅰ)或(Ⅱ)的一个周期解,进而得到二阶Hamilton系统的一个满足所述初始条件的解的存在性定理.
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| 关 键 词： | 二阶系统 周期解 临界点 |
Existence of Periodic Solution for Second Order Hamiltonian Systems with Obstacles |
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| WANG Shao-min,XIONG Ming.Existence of Periodic Solution for Second Order Hamiltonian Systems with Obstacles[J].Journal of Hunan Institute of Science and Technology,2012(1):12-15,56. |
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| Authors: | WANG Shao-min XIONG Ming |
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| Institution: | (Department of Mathematics and Computer Science,Dali University,Dali 671003,China) |
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| Abstract: | The main purpose of this dissertation is to study the existence of periodic solutions for the following second order Hamiltonian systems:-=f(t,x) Satisfying the following conditions: x(t)≥0,t∈R,(t0-)=(t0+),if x(t0)=0 Since in some conditions,the above systems are equivalent to the following systems:{-=f(t,|x|)sgn(x),x(0)-x(2π)=(0)-(2π)=0(Ⅰ){-=f(t,|x|)sgn(x),x(0)-x(2π)=(0)-(2π)=0 (Ⅱ) So,in this dissertation,we obtain a existence theorem of the second order Hamiltonian systems by researching the periodic solutions of system(I) or(II) via a new critcal points theorem of locally Lipschitz functions. |
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| Keywords: | second order Hamiltonian system periodic solution critical point |
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