Abstract
A linear ordinary differential operator with bounded coefficients satisfying certain homogeneous initial conditions is shown to be invertible onL 2n (0, ∞) if and only if the underlying system of differential equations has a dichotomy. Moreover, in that case the operator is proved to be a direct sum of two infinitesimal generators ofC 0-semigroups, one of which has support on the negative half-line and the other on the positive half-line. The effect of perturbations of the initial values on the dichotomy is also described.
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Ben-Artzi, A., Gohberg, I. & Kaashoek, M.A. Invertibility and dichotomy of differential operators on a half-line. J Dyn Diff Equat 5, 1–36 (1993). https://doi.org/10.1007/BF01063733
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DOI: https://doi.org/10.1007/BF01063733