| 具有势函数的高阶非线性Schr(o)dinger方程的解 |
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| 引用本文： | 郭翠花,崔尚斌.具有势函数的高阶非线性Schr(o)dinger方程的解[J].中山大学学报(自然科学版),2005,44(5):10-13. |
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| 作者姓名： | 郭翠花 崔尚斌 |
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| 作者单位： | 中山大学数学系,广东,广州,510275 |
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| 摘 要： | 研究了一个带有与时间t有关的势函数的高阶Schrdinger方程初值问题的解的存在性,唯一性与正则性,给出了能使方程有古典解的势函数的充分条件.在第一种假设下用压缩不动点原理给出了解的局部存在性,再利用能量守恒律得到了解的整体存在性.在第二种假设下用磨光函数得到了解的存在性.
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| 关 键 词： | Schr(o)dinger方程 初值问题 势函数 |
| 文章编号： | 0529-6579(2005)05-0010-04 |
| 收稿时间： | 09 22 2004 12:00AM |
| 修稿时间： | 2004年9月22日 |
Solutions for Higher-order Schr(o)dinger Equation with Potentials |
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| GUO Cui-hua,CUI Shang-bin.Solutions for Higher-order Schr(o)dinger Equation with Potentials[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2005,44(5):10-13. |
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| Authors: | GUO Cui-hua CUI Shang-bin |
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| Institution: | Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China |
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| Abstract: | The existence, uniqueness and the regularity for the solutions of the initial value problem for the higher-order Schrodinger equation with the time dependent potentials are discussed. The sufficient conditions on potential function ate given so that this equation has classical solutions. Under the first assumption, the local solution is obtained by using fixed point theorem; the global solution is obtained by using the energy conservation laws. Under the second assumption, the solution is obtained by making moliphier functions. |
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| Keywords: | Schrodinger equation initial value problem potential function |
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