| 一类高阶微分方程周期解的存在唯一性 |
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| 引用本文： | 冯艳青,王忠英.一类高阶微分方程周期解的存在唯一性[J].常州工学院学报,2011,24(1):47-49. |
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| 作者姓名： | 冯艳青 王忠英 |
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| 作者单位： | 常州工学院理学院; |
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| 基金项目： | 常州工学院自然科学基金(YN0909) |
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| 摘 要： | 通过引入非负强制函数,利用全局同胚理论证明了2k阶微分方程kΣj=1αju(2j)(t)+(-1)k+1f(x,u(t))=0(x∈Rn,αj是常数)周期解存在的充分条件,证明定理1是定理3的推论.
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| 关 键 词： | 非负强制函数 周期解 全局同胚 |
The Existence and Uniqueness of Periodic Solution to a 2k Higher Order Differential Equation |
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| FENG Yan-qing,WANG Zhong-ying.The Existence and Uniqueness of Periodic Solution to a 2k Higher Order Differential Equation[J].Journal of Changzhou Institute of Technology,2011,24(1):47-49. |
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| Authors: | FENG Yan-qing WANG Zhong-ying |
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| Affiliation: | FENG Yan-qing WANG Zhong-ying(School of Science,Changzhou Institute of Technology,Changzhou 213002) |
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| Abstract: | By the introduction of nonnegative auxiliary scalar coercive function,and the use of a global inverse theorem,this paper proves the sufficient condition of the existence 2k(∑kj=1αju(2j)(t)+(-1)k+1f(x,u(t))=0) periodic solution and proves that theorem 1 is the inference of theorem 3. |
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| Keywords: | nonnegative auxiliary scalar coercive function periodic solution homeomorphism |
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