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Nonlinear Perron-Frobenius problem for order-preserving mappings. I. (English) Zbl 0797.47034

Summary: We consider the eigenvalue problem of an order-preserving mapping defined on a positive cone of an ordered Banach space. Among other things, we prove the existence and, in some cases, the uniqueness of the positive eigenvalue. We also discuss other properties of eigenvalues and eigenvectors. The notion of indecomposability for nonlinear mappings that we introduce in an infinite dimensional setting will play a key role in our argument. We apply the results in this paper to boundary value problems for a class of partial differential equations in part II (cf. review below).

MSC:

47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces

Citations:

Zbl 0797.47035
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References:

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