| 一类非线性算子方程的求解方法 |
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| 引用本文： | 李春利,崔明根. 一类非线性算子方程的求解方法[J]. 计算数学, 2003, 25(2): 185-192 |
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| 作者姓名： | 李春利 崔明根 |
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| 作者单位： | 哈尔滨工业大学数学系,哈尔滨,150001;哈尔滨工业大学数学系,哈尔滨,150001 |
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| 摘 要： | 1.引言首先研究线性方程Au=f (1.1)的求解问题,其中A是H→H的连续线性算子,H是可分Hilbert空间,U,f∈H,||f||=1.利用得到的结论,研究一类非线性算子方程AuBu+Cu=f(1.2)
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| 关 键 词： | 非线性算子方程 再生核空间 线性算子方程 |
| 修稿时间： | 2001-03-18 |
THE METHODS SOLVING A CLASS NONLINEAR OPERATOR EQUATIONS |
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| Li Chunli Cui Minggen. THE METHODS SOLVING A CLASS NONLINEAR OPERATOR EQUATIONS[J]. Mathematica Numerica Sinica, 2003, 25(2): 185-192 |
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| Authors: | Li Chunli Cui Minggen |
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| Affiliation: | Li Chunli Cui Minggen (Dept. of Math., Harbin Inst. of Technology, Harbin, 150001) |
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| Abstract: | The necessary and sufficient condition for the existence and the uniqueness ofsolution of the continuous linear operator equation is given. We give also minimalnorm solution(or generalized) of the equation. Further, we construct a reproducingkernel space W21(Ω)and give the reproducing kerne of the space W21(Ω). In thespace W21(Ω), we study the problem of solving a class nonlinear operator equation.Some examples are also given illustrate of this theory. |
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| Keywords: | nonlinear operator equation reproducing kernel linear operator equation |
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