, Volume 54, Issue 11, pp 1842-1858

Solutions of Weakly-Perturbed Linear Systems Bounded on the Entire Axis

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We establish conditions under which solutions of weakly-perturbed systems of linear ordinary differential equations bounded on the entire axis R emerge from the point ε = 0 in the case where the corresponding unperturbed homogeneous linear differential system is exponentially dichotomous on the semiaxes R + and R .