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Fixed points of cone-compressing and cone-extending operators in Fréchet spaces. (English) Zbl 1041.47040

The aim of this interesting paper is to present a generalization of the well-known cone-compression and cone-expansion fixed point theorem (due to Krasnosel’skii) for the case of a completely continuous and admissible single-valued map on a Fréchet space. As an application, an existence result for a nontrivial solution of a second-order differential equation on the half-line is also established.

MSC:

47H10 Fixed-point theorems
34B40 Boundary value problems on infinite intervals for ordinary differential equations
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