| 非线性方程分歧理论中广义Lyapunov-Schmidt过程及应用 |
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| 引用本文： | 孙秀梅,殷洪才,王玉文.非线性方程分歧理论中广义Lyapunov-Schmidt过程及应用[J].数学的实践与认识,2003,33(5):108-114. |
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| 作者姓名： | 孙秀梅 殷洪才 王玉文 |
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| 作者单位： | 哈尔滨师范大学数学系,黑龙江,哈尔滨,150080 |
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| 基金项目： | 国家自然科学基金 (批准号 :1 9971 0 2 3)，黑龙江省自然科学基金，黑龙江省教育厅海外学人科研基金资助项目 |
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| 摘 要： | 本文讨论带有参数的算子方程 f ( x,λ) =0的分歧问题 ,其中 f :X×Λ→ Y,X,Y为 Banach空间 ,Λ =R为参数空间 .利用 A =f′x( x0 ,λ0 )的有界线性广义逆 A+ ,引入广义 Lyapunov-Schmidt过程 ,当 A为 Fredholm算子时 ,这种广义 Lyapunov-Schmidt过程就成为通常的 Lyapunov-Schmidt过程 .本文利用所引进的广义Lyapunov-Schmidt过程 ,证得关于抽象方程 f ( x,λ) =0的一个分歧定理 .
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| 关 键 词： | Banach空间 算子方程 分歧理论 算子广义逆 广义Lyapunov-Schmidt过程 |
| 修稿时间： | 2003年2月20日 |
The Generalized Lyapunov-Schmidt Process in the Bifurcation Theory of Nonlinear Operator Equation |
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| SUN Xiu-mei,YIN Hong-cai,WANG Yu-wen.The Generalized Lyapunov-Schmidt Process in the Bifurcation Theory of Nonlinear Operator Equation[J].Mathematics in Practice and Theory,2003,33(5):108-114. |
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| Authors: | SUN Xiu-mei YIN Hong-cai WANG Yu-wen |
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| Abstract: | This paper intends to discuss the bifurcation problem of the nonlinear operator equation with the form f(x,λ)=0, where f:X×Λ→Y is C′-mapping, X,Y are Banach spaces, Λ=R′ is a parameter space.;Let A=f′ x(x 0,λ 0). We introduce a generalized Lyapunov-Schmidt process by means of the bounded linear generalized inverse A+ of A. If A is a Fredholm operator, the generalized Lyapunov-Schmidt process becomes the Lyapunov-Schmidt process as usual. By the generalized Lyapunov-Schmidt process, a abstract bifurcation theorem for the nonlinear operator equation has been obtained in this paper. |
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| Keywords: | Banach space operator equation bifurcation theory generalized inverse generalized Lyapunov-Schmidt process |
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