Almost regularity conditions of spectral problems for a second order equation

TL;DR

This paper derives exact asymptotic distributions for solutions of second-order spectral problems, establishes recursive formulas for coefficients, and proves necessary and sufficient conditions for almost regularity of these spectral problems.

Contribution

It introduces recursive formulas for asymptotic coefficients and proves conditions for almost regularity in second-order spectral problems.

Findings

Exact asymptotic distributions for solutions derived

Recursive formulas for asymptotic coefficients obtained

Necessary and sufficient conditions for almost regularity proved

Abstract

In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using obtained recurent formulas the neccessary and sufficient conditions almost regularity of spectral problem for the equation of the second order is proved.