Author:
Savchuk A. M.,Shkalikov A. A.
Abstract
Abstract
Ordinary differential equations of the form
on the finite interval
are under consideration. Here the functions
and
are absolutely continuous and positive and the coefficients of the differential expression
are subject to the conditions
where
denotes the
th antiderivative of the function
in the sense of distributions. Our purpose is to derive analogues of the classical asymptotic Birkhoff-type representations for the fundamental system of solutions of the above equation with respect to the spectral parameter as
in certain sectors of the complex plane
. We reduce this equation to a system of first-order equations of the form
where
is a positive function,
is a matrix with constant elements, the elements of the matrices
and
are integrable functions, and
as
. For systems of this kind, we obtain new results concerning the asymptotic representation of the fundamental solution matrix, which we use to make an asymptotic analysis of the above scalar equations of high order.
Bibliography: 44 titles.
Funder
Russian Science Foundation
Subject
Algebra and Number Theory
Cited by
13 articles.
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