具公共值的Fredholm紧映射

J. M. 索里阿诺

具公共值的Fredholm紧映射

J. M. 索里阿诺

塞维拉大学数学学院数学系, 塞维拉41080, 西班牙

基金项目: D.G.E.S.PB基金资助项目(96-1338-CO2-01);Junta de Andalucia基金

详细信息

中图分类号: O177.2;O192
计量
- 文章访问数: 2011
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- 被引次数: 0
出版历程
- 收稿日期: 2000-11-22
- 刊出日期: 2001-06-15

Fredholm and Compact Mappings Sharing a Value

J. M. Soriano

Departmento de Anûlisis Matemûtico, Facultad de Matemûticas, Universidad de Sevilla, Aptdo 1160, Sevilla 41080, Spain

摘要

摘要: 给出了Banach空间之间的两个可微映射具有公共值的充分条件,证明的方法本质上是基于延拓法。
- 延拓法 /
- C¹-同伦 /
- 满射 /
- 隐函数定理 /
- 紧映射 /
- Fredholm映射 /
- 零指数 /
- 单射 /
- 微分同胚
Abstract: Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values.The proof is essentially based upon continuation methods.
- zero point /
- continuation methods /
- C¹-homotopy /
- surjective implicit-function theorem /
- compact mapping /
- Fredholm mapping /
- index zero /
- injective /
- diffeomorphism

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参考文献(20)

[1]	Allgower E L, Georg K. Numerical Cont inuation Method[M]. Springer Series in Computational Mathematics 13.New York: Springer-Verlag,1990.
[2]	Allgower E, Clashoff K, Peitgen H. A Survey of Homotopy Methods for Smooth Mappings[M]. Berlin: Springer-Verlag,1981,2-29.
[3]	Allgower E, Glashoff K, Peitgen H. A survey of homotopy methods for smooth mappings[A]. In: Proceedings of the Conference on Numerical Solutions of Nonlinear Equations[C]. Bremen, July,1980,Lecture Notes in Math[M]. 878.Berlin: Springer-Verlag,1981,1-29.
[4]	Alexander J C, York J A. Homotopy continuation methods: numerically implementable topological procedures[J]. Trans Amer Math Soc,1978,242:271-284.
[5]	Bernstein S. Surla generalisation du problème de Dirichlet Ⅰ[J]. Math Anal,1906,62:253-270.
[6]	Bernstein S. Surla generalisation duproblème de Dirichlet Ⅱ[J]. Math Anal,1910,69:82-136.
[7]	Leray J, Shauder J. Topologie et equations of fonctionalle s[J]. Ann Sci Ecole Norm Sup,1934,51:45-78.
[8]	Garcia C B, Li. On the number of solutions to polynomial systems of nonlinear equations[J]. SIAM J Numer Anal,1980,17:540-546.
[9]	Garcia C B, Zangwill W I. Determining all solutions to certain systems of nonlinear equations[J]. Math Oper Res,1979,4:1-14.
[10]	Zeidler E. Nonlinear Functional Analysis and Its Applications [M]. New York: Springer-Verlag,1985.
[11]	Soriano J M. Global minimum point of a convex function[J]. Appl Math Comput,1993,55(2-3):213-218.
[12]	Soriano J M. Extremum points of a convex function[J]. Appl Math Comput,1994,66:261-266.
[13]	Soriano J M. On the existence of zero points[J]. Appl Math Comput,1996,79:99-104.
[14]	Soriano J M. On the number of zeros of a mapping[J]. Appl Math Comput,1997,88:287-291.
[15]	Soriano J M. Existence of zeros for bounded perturbations of prop er mappings[J]. Appl Math Comput,1999,99:255-259.
[16]	Soriano J M. Mappings sharing a value on finite-dimensional spaces[J]. Appl Math Comput,(pending publication)
[17]	Soriano J M. On the Bezout theorem real case[J]. Appl Nonlinear Anal,1995,2(4):59-66.
[18]	Soriano J M. On the Bezout theorem[J]. Commun Nonlinear Anal,1997,4(2):59-66.
[19]	Soriano J M. Zeros of compact perturbations of proper mappings[J]. Appl Nonlinear Anal,2000,7(4):31-37.
[20]	Soriano J M. Compact mappings and proper mappings between Banach spaces which share a value[J]. Math Balkanica,2000,14(1) (2).