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Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations
查看参考文献8篇
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文摘
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We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first–order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution. |
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来源
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Acta Mathematica Sinica. English Series
,2007,23(12):2205-2212 【核心库】
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DOI
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10.1007/s10114-005-0769-0
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关键词
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fixed point
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partially ordered set
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first-order differential equation
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lower and upper solutions
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地址
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Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela
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语种
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英文 |
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ISSN
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1439-8516 |
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学科
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数学 |
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基金
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Xunta de Galicia and FEDER
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Projects PGIDIT02PXIC20703PN
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Project MTM2004-06652-C03-01
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Ministerio de Educación y Ciencia and FEDER
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Projects PGIDIT05PXIC20702PN
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文献收藏号
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CSCD:3144612
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参考文献 共
8
共1页
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1.
Ran A C M. A. xed point theorem in partially ordered sets and some applications to matrix equations.
Proc. Amer. Math. Soc.,2004,132:1435-1443
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CSCD被引
20
次
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2.
Nieto J J. Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations.
Order,2005,22:223-239
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CSCD被引
12
次
|
|
|
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3.
Tarski A. A lattice-theoretical fixpoint theorem and its applications.
Pacific J. Math.,1955,5:285-309
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CSCD被引
33
次
|
|
|
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4.
Cousot P. Constructive versions of Tarski’s fixed point theorems.
Pacific J. Math.,1979,82:43-57
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CSCD被引
2
次
|
|
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5.
Zeidler E.
Nonlinear functional Analysis and its applications, Vol I:Fixed-Point Theorems,1986
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CSCD被引
1
次
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6.
Amann H.
Order structures and fixed points, Bochum:Mimeographed lecture notes,1977
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CSCD被引
1
次
|
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7.
Heikkila S.
Monotone iterative techniques for discontinuous nonlinear differential equations,1994
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CSCD被引
6
次
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8.
Ladde G S.
Monotone iterative techniques for nonlinear differential equations,1985
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CSCD被引
30
次
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