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Three positive fixed points of nonlinear operators on ordered banach spaces

โœ Scribed by R.I. Avery; A.C. Peterson

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
331 KB
Volume
42
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

We generalize the fixed-point theorem of Leggett-Williams, which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a Banach space. We then show how to apply our theorem to prove the existence of three positive solutions to a second-order discrete boundary value problem.

๐Ÿ“œ SIMILAR VOLUMES

Fixed points of decreasing operators in
Fixed points of decreasing operators in ordered Banach spaces and applications to nonlinear second order elliptic equations
โœ Zengqin Zhao; Xiangping Chen ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 449 KB

In this paper, we consider some decreasing operators in ordered Banach spaces. We study the existence and uniqueness of fixed points and properties of the iterative sequences for these operators. Lastly, the results are applied to nonlinear second order elliptic equations.