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A fixed-point theorem for S-type operators on Banach spaces and its applications to boundary-value problems. (English) Zbl 1182.47042

The main result of this paper is a fixed point theorem for an \(S\)-type completely continuous operator on a cone \(K\) in a Banach space. As an application, an existence result for positive solutions of two boundary value problems are given.

MSC:

47H10 Fixed-point theorems
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47N20 Applications of operator theory to differential and integral equations
34K10 Boundary value problems for functional-differential equations
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