The notion of lp trichotomy for a linear difference system is here considered as extension of exponential trichotomy and lp dichotomy. The main properties are analyzed and necessary and sufficient conditions for the existence are given. The asymptotic behavior of solutions of a quasilinear system x(n + 1) = A(n)x(n) + f(n; x(n)) is studied under the assumption that the associated linear system possesses a lp trichotomy.
THE L^P TRICHOTOMY FOR DIFFERENCE SYSTEMS AND APPLICATIONS / S. MATUCCI. - In: ARCHIVUM MATHEMATICUM. - ISSN 0044-8753. - STAMPA. - 36 (5):(2000), pp. 519-529.
THE L^P TRICHOTOMY FOR DIFFERENCE SYSTEMS AND APPLICATIONS
MATUCCI, SERENA
2000
Abstract
The notion of lp trichotomy for a linear difference system is here considered as extension of exponential trichotomy and lp dichotomy. The main properties are analyzed and necessary and sufficient conditions for the existence are given. The asymptotic behavior of solutions of a quasilinear system x(n + 1) = A(n)x(n) + f(n; x(n)) is studied under the assumption that the associated linear system possesses a lp trichotomy.
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