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Fixed points of increasing operators in ordered Banach spaces and applications. (English) Zbl 0671.47054
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:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
34G20Nonlinear ODE in abstract spaces
47H07Monotone and positive operators on ordered topological linear spaces