| 二阶常微分方程边值问题的适定性 |
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| 引用本文： | 赵晓云. 二阶常微分方程边值问题的适定性[J]. 阜阳师范学院学报(自然科学版), 2011, 28(4): 32-34 |
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| 作者姓名： | 赵晓云 |
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| 作者单位： | 阜阳师范学院物理与电子科学学院,安徽阜阳,236041 |
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| 基金项目： | 安徽省精品课程(数学物理方法);教育部高等学校特色专业(物理学)建设点项目资助 |
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| 摘 要： | 通过与初值问题的比较，研究了二阶线性常微分方程边值问题的适定性。当泛定方程的通解已经求得后，定解问题就转化为解空间中的线性方程组。该方程组的系数由定解条件确定，与定解问题具有同样的适定性。如果由定解问题转化的线性方程组的系数行列式不等于零，那么该边值问题存在唯一解，否则边值问题不适定。
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| 关 键 词： | 常微分方程 边值问题 适定性 |
Well-posedness of boundary-value problems for the 2-order ordinary differential equations |
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| ZHAO Xiao-yun. Well-posedness of boundary-value problems for the 2-order ordinary differential equations[J]. Journal of Fuyang Teachers College:Natural Science, 2011, 28(4): 32-34 |
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| Authors: | ZHAO Xiao-yun |
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| Affiliation: | ZHAO Xiao-yun (School of Physics and Electronic Science,Fuyang Teachers College,Fuyang Anhui 236041,China) |
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| Abstract: | Well-posedness of boundary value problems for the second-order linear ordinary differential equations is discussed through the comparison with initial value problem.When general solution of a pan-setting equation is obtained,fixed solution problem will be transformed into the linear equations of solution spaces.The coefficients of the linear equations are determined by definite conditions.And the solutions of the coefficients have the same well-posedness as a fixed solution problem.If the coefficient determinant of the linear equations is not zero,then there exist unique solutions to the boundary value problems,otherwise the boundary value problem is ill-posed. |
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| Keywords: | ordinary differential equation boundary-value problems well-posedness |
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