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Functional expansion - compression fixed point theorem of Leggett-Williams type [PDF]
Electronic Journal of Differential Equations, 2010 This paper presents a fixed point theorem of compression and expansion of functional type in the spirit of the original fixed point work of Leggett-Williams.
Douglas R. Anderson +2 more
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Two modifications of the Leggett-Williams fixed point theorem and their applications [PDF]
Electronic Journal of Differential Equations, 2010 This article presents two modifications of the Leggett-Williams fixed point theorem, and two applications of these results to a terminal and to a boundary value problem for ordinary differential equations.
Kyriakos G. Mavridis
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Leggett-Williams fixed point theorem type for sums of operators and application in PDEs [PDF]
Differential Equations and Applications, 2021 Summary: In this paper we present an extension of the original version of Leggett-Williams fixed point theorem for a \(k\)-set contraction perturbed by an expansive operator. Our approach is applied to prove the existence of non trivial positive solutions for initial value problems (IVPs for short) covering a class two-dimensional nonlinear wave ...
Svetlin Georgiev, Karima Mebarki
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Fixed point theorem of Leggett–Williams type and its application
Journal of Mathematical Analysis and Applications, 2004 One of the generalizations of Krasnoselskii's theorem on cone expansion and compression was obtained in [\textit{R. W. Leggett, L. R. Williams}, J. Math. Anal. Appl., Vol. 76, 91--97 (1980; Zbl 0448.47044)]. In the present paper, the author proves the following Leggett-Williams type theorem: Theorem.
Mirosława Zima
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Some fixed point theorems of Leggett-Williams type
Rocky Mountain Journal of Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Johnny Henderson +2 more
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Generalization for Amann's and Leggett–Williams' three-solution theorems and applications
Journal of Mathematical Analysis and Applications, 2004 Let \(X\) be a nonempty closed convex subset of a real ordered Banach space \(E\) and \(A:X \to X\) a completely continuous operator. The authors give conditions for \(A\) to have at least three fixed points. The results generalize those of \textit{H. Amann} [J. Funct. Anal. 11, 346--384 (1972; Zbl 0244.47046)], \textit{R. W. Leggett} and \textit{L. R.
Guodong Han
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Rocky Mountain Journal of Mathematics, 2001 Criteria are developed for the existence of three nonnegative solutions to integral and discrete equations. The strategy involves using the Leggett Williams fixed point theorem.
Donal O'Regan, Ravi Agarwal
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A Dual of the Compression-Expansion Fixed Point Theorems
Fixed Point Theory and Applications, 2007 This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multi-valued situation is also discussed.
Donal O'Regan +2 more
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Fixed point theorem utilizing operators and functionals
Electronic Journal of Qualitative Theory of Differential Equations, 2012 This paper presents a fixed point theorem utilizing operators and functionals in the spirit of the original Leggett-Williams fixed point theorem which is void of any invariance-like conditions.
Douglas Anderson +3 more
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Fractal and Fractional, 2023 In this paper, by using the Leggett–Williams fixed-point theorem, we study the existence of positive solutions to fractional differential equations with mixed Riemann–Liouville and quantum fractional derivatives.
Nemat Nyamoradi +2 more
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