| Liouville—Hill方程的算子解法及应用 |
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| 引用本文： | 谈骏渝.Liouville—Hill方程的算子解法及应用[J].重庆大学学报(自然科学版),1993,16(5):131-136. |
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| 作者姓名： | 谈骏渝 |
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| 作者单位： | 重庆大学系统工程及应用数学系 重庆，630044 |
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| 摘 要： | 对Ｌｉｏｕｖｉｌｌｅ－Ｈｉｌｌ方程，应用算子解法给出了级数解的递推公式，讨论了级数余项及估计，从而得到了解的存在和唯一性。进一步，讨论了具有尼项的非齐次项Ｈｉｌｌ方程的初值问题即受迫振动问题，给出了级数解及收敛的充分条件。
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| 关 键 词： | 算子 初值问题 收敛性 L－H方程 |
The Operator Solution of Liouville-Hill Equation and Its Applications |
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| Tan Junyu.The Operator Solution of Liouville-Hill Equation and Its Applications[J].Journal of Chongqing University(Natural Science Edition),1993,16(5):131-136. |
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| Authors: | Tan Junyu |
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| Abstract: | With operator solution. recursion formula of series solution to Liouville-Hill equation is given, furthermore the paper discusses the remainder term of the series and its estimation. and the existence and uniqueness of the solution is obtianed. Next,we discuss the inital problem of the n on homogeneous Hill equation with damping terms, which is a forced oscillation problem, and the series sloution and the sufficient conditions of its convergence are also given. |
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| Keywords: | operator initial value problem series solution existence and uniqueness Con-vergence |
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