Generalized communication conditions and the eigenvalue problem for a monotone and homogeneous function. (English) Zbl 1208.47059

Cavazos-Cadena, Rolando

Kybernetika 46, No. 4, 665-683 (2010).

The author obtains a nonlinear version of the Perron-Frobenius theorem in the case of an eigenvalue problem involving a monotone and homogeneous self-mapping of a finite-dimensional positive cone. The approach relies on the study of the notions of projectively bounded and invariant sets.

Reviewer: Dumitru Motreanu (Perpignan)

MSC:

47J10	Nonlinear spectral theory, nonlinear eigenvalue problems
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H07	Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces

Keywords:

projectively bounded and invariant sets; generalized Perron-Frobenius conditions; nonlinear eigenvalue; Collatz-Wielandt relations

References:

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