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

Ivanov, B. A.

Sib. Mat. Zh. 26, No. 5(153), 86-93 (1985).

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

Keywords:

positive operator function; Banach space with a cone; ”positive” eigenvalues of the spectral problem; Variational properties; iterative method; minimal positive eigenvalue