On Γ-limit classes of perturbations defined by integral conditions

Abstract

For the coefficients of linear differential systems, we consider classes of piecewise continuous perturbations that are infinitesimal in mean on the positive half-line with some positive piecewise continuous weight belonging to a given set. We obtain sufficient conditions for such a class to be Γ-limit, i.e., to admit the computation of a reachable upper bound of the exponents of linear differential systems with perturbations in that class by a formula similar to the well-known formulas for the central and exponential exponents.