## Variation properties of the spectrum of positive operator functions.(Russian)Zbl 0585.47011

For a given positive operator function $$Q_{\lambda}$$, $$\lambda\in (\alpha,\beta)$$, in a Banach space with a cone, ”positive” eigenvalues of the spectral problem $$x-Q_{\lambda}x=0$$ (x$$\geq 0)$$ are considered. Variational properties of such eigenvalues are investigated. An iterative method is given for finding a minimal positive eigenvalue.
Reviewer: A.Pankov

### MSC:

 47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 47B60 Linear operators on ordered spaces 47A10 Spectrum, resolvent 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 46B42 Banach lattices
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