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Dichotomies and moving singularities

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Abstract

We consider a linear differential system εσ Φ (t,ε)Y′ =A(t, ε)Y, with ε a small parameter and Φ(t, ε) a function which may vanish in the domain of definition. Under some conditions imposed on the eigenvalues of the matrixA(t, ε), there exists an invertible matrixH(t, ε) which is continuous on ([0,a] × [0, ε0]). The transformationY=H(t, ε)Z takes then dimensional linear system into two differential systems of orderk andn−k respectively, withk<n. Thus the investigaton ofn dimensional systems encountered in singular perturbation as well as in stability theory is considerably simplified.

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  1. Western Michigan University, 49008, Kalamazoo, MI, U.S.A.

    H. Gingold

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  1. H. Gingold
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Gingold, H. Dichotomies and moving singularities. Rend. Circ. Mat. Palermo 29, 61–78 (1980). https://doi.org/10.1007/BF02844395

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