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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:
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
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References:
[1] Amann H., J. Punct. Anal 11 pp 346– (1972) · Zbl 0244.47046
[2] Ando T., Pacific J.Math 12 pp 1163– (1962) · Zbl 0123.30802
[3] Hoft D., canad. J.Math 28 pp 992– (1976) · Zbl 0321.06002
[4] Krasnoselskii M.A., Positive solutions of Operator Equations (1964)
[5] Ladde G.A., iterativeTechniques for Nonlinear Differential Equations (1985)
[6] Jingxin bun, Appl. Anal 23 pp 23– (1966) · Zbl 0585.47046
[7] Bajun Quo, J. Math. Anal. Appl 129 pp 211– (1968)
[8] Laetsch Nonlinear eigenvalue problems with positive convex operators, 51 129 pp 653– (1975)
[9] Du S.W., J. Math. Anal. Appl 87 pp 454– (1982) · Zbl 0523.34057
[10] Deimling K., Lecture Notes in Math 596 (1977)
[11] Dajun Quo, Nonlinear problems in Abstract .Cones (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.