ASYMPTOTICS OF SOLUTIONS TO EQUATIONS OF NEUTRAL TYPE

Authors

  • S. Alejdarov Dagestan State University

Keywords:

neutral type, power weight, solvability, Hilbert space

Abstract

In this article, we consider an equation of neutral type with linear deviation of the argument in a Hilbert space with a power-law weight. The presence of a linear deviation of the argument and a variable coefficient in front of the derivative does not allow the Fourier transform to be applied to study an equation of neutral type. Therefore, when considering questions of solvability and asymptotics, we used the Mellin transform.
For an equation of neutral type with constant operator coefficients, sufficient conditions are obtained for unique solvability through the resolvent.
For an equation of neutral type with variable coefficients, estimates of the variable parts are obtained that provide unique solvability.
An asymptotic estimate is obtained for all solutions of the equation in the case when the solution is not unique.

References

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Published

2021-08-11

Issue

Vol. 1 No. 69 (2021)

Section

Статьи

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