A dynamical systems result on asymptotic integration of linear differential systems. (Q1864645)

The author studies, under a dynamical systems point of view, the asymptotic integration of linear differential systems of the form \(x^{\prime }=[\Lambda (t)+R(t)]x\), where \(\Lambda \) is diagonal and \(R\in L^{p}[t_{0},\infty )\) for \(p\in [ 1,2]\). By using the theory of linear skew-product flows, the paper presents a dichotomy condition in terms of the spectrum over the omega-limit set \(w_{\Lambda }\). The theory is illustrated by two examples that are not covered by the Hartman-Winter theorem.