Abstract. The notion of $l^p$ trichotomy for a linear difference system is here considered as extension of exponential trichotomy and $l^p$ dichotomy. The main properties are analyzed and necessary and sufficient conditions for the existence are given. The asymptotic behavior of solutions of a quasi-linear system $x(n+1) = A(n) x(n) + f(n, x(n))$ is studied under the assumption that the associated linear system possesses a $l^p$ trichotomy.
AMSclassification. 39A10, 39A11, 39A12
Keywords. Nonlinear difference systems, asymptotic behavior of solutions, $l^p$ trichotomy