Abstract
We study a functional-differential equation
, whereF is a linear operator acting from the Hölder spaceH γ into the Sobolev space W sp [0, 1] and ρ is a complex parameter. For large absolute values of ρ, we construct a one-to-one correspondence between the solutionsx(ρ;t) andy(ρ;t) of the equations
andy (n)+ρy n=0. We also establish conditions that should be imposed on the operatorF in order that specially selected fundamental systems of solutions of these equationsx j (ρ;t) andy j (ρ;t), j=1,...,n, satisfy the estimate
with constantsc, κ>0 for the functional space
=W lq [0, 1] or
.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 811–836, June, 1995.
This work was financially supported by the International Science Foundation and the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.
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Radzievskii, G.V. Asymptotics of the fundamental system of solutions of a linear functional-differential equation with respect to a parameter. Ukr Math J 47, 936–962 (1995). https://doi.org/10.1007/BF01058784
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DOI: https://doi.org/10.1007/BF01058784