Fixed points of increasing operators in ordered Banach spaces and applications. (English) Zbl 0671.47054

Du, Yihong

Appl. Anal. 38, No. 1-2, 1-20 (1990).

We prove some fixed point theorem of increasing operators which map an order interval into itself. Compactness conditions on the operator are removed by assuming the space to be weakly complete or assuming the operator to have some concavity or convexity properties. Some results of M. A. Krasnosel’skij and H. Amann are generalized. The abstract results are used to get some existence theorems for nonlinear ODEs in ordered Banach spaces.

Reviewer: Du Yihong

MSC:

47H10	Fixed-point theorems
34G20	Nonlinear differential equations in abstract spaces
47H07	Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces

Keywords:

fixed point theorem of increasing operators which map an order interval into itself; compactness; concavity or convexity properties; nonlinear ODEs in ordered Banach spaces

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