A variant of the Krein-Rutman theorem for Poincaré difference equations

摘要

Let , , be a non-vanishing solution of the Poincaré difference equation where A _n , , are real matrices such that the limit exists (entrywise). According to a Perron type theorem, the limit exists and is equal to the modulus of one of the eigenvalues of A. In this paper, we show that if the solution belongs to a given order cone K in , then is an eigenvalue of A with an eigenvector in K. In the case of constant coefficients, this result implies the finite-dimensional version of the Krein-Rutman theorem.View full textDownload full textKeywordsPoincaré difference equation, order cone, Krein-Rutman theorem, quasilinear equationKeywords39A10, 39A21, 39A22, 15B48Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/10236198.2011.594439