Abstract

We develop our earlier generalizations of the Perron effect of change of values of characteristic exponents for arbitrary parameters m > 1 and λ1 ≤ λ2 1 in a neighborhood of the origin and possibly growing outside the neighborhood such that the nontrivial solutions of the perturbed system are infinitely extendible and the characteristic exponents of solutions issuing from any neighborhood of the origin form exactly the set β. In addition, we generalize this infinite version of the Perron effect in a neighborhood of the origin to other points of the plane of initial values of solutions.

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