On an Interior Compactness of One Homogeneous Boundary Value Problem

TL;DR

This paper establishes conditions for the existence and uniqueness of regular solutions to a boundary value problem involving second-order homogeneous operator-differential equations with singular coefficients, focusing on spectral properties of the normal operator.

Contribution

It provides new criteria ensuring solution existence and uniqueness for a class of boundary value problems with singular coefficients and spectral constraints.

Findings

Conditions for existence and uniqueness are derived.

Spectral properties of the normal operator are characterized.

Solutions are shown to be regular under specified conditions.

Abstract

In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of the equation contains the normal operator the spectrum of which is contained in the certain sectors.