Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1140.47045
Nieto, Juan J.; Rodr{\'\i}guez-López, Rosana
Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. (English)
[J] Acta Math. Sin., Engl. Ser. 23, No. 12, 2205-2212 (2007). ISSN 1439-8516; ISSN 1439-7617/e

Summary: 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 [Order 22, No.\,3, 223--239 (2005; Zbl 1095.47013)], 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.

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H07 Positive operators on ordered topological linear spaces
47N20 Appl. of operator theory to differential and integral equations
34B15 Nonlinear boundary value problems of ODE

Keywords: fixed point; partially ordered set; first-order differential equation; lower and upper solutions

Citations: Zbl 1095.47013

Cited in: Zbl 1204.54037 Zbl 1171.28002 Zbl 1142.47033

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]