2019
Том 71
№ 11

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Asymptotics of the fundamental system of solutions of a linear functional-differential equation with respect to a parameter

Radzievskii G. V.

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Abstract

We study a functional-differential equation, where F is a linear operator acting from the Hölder space Hγ into the Sobolev space W p s [0, 1] and ρ is a complex parameter. For large absolute values of ρ, we construct a one-to-one correspondence between the solutions x(ρ;t) and y(ρ;t) of the equations and y(n)+ρyn=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.

English version (Springer): Ukrainian Mathematical Journal 47 (1995), no. 6, pp 936-962.

Citation Example: Radzievskii G. V. Asymptotics of the fundamental system of solutions of a linear functional-differential equation with respect to a parameter // Ukr. Mat. Zh. - 1995. - 47, № 6. - pp. 811–836.

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