Fredholm one-dimensional boundary-value problems in Sobolev spaces

TL;DR

This paper investigates the solvability and well-posedness of general linear boundary-value problems for systems of ODEs in Sobolev spaces, providing indices and solvability criteria.

Contribution

It introduces a comprehensive analysis of boundary-value problems in Sobolev spaces, including indices and solvability criteria, for the first time in this context.

Findings

Derived indices for boundary-value problems

Established criteria for well-posedness

Analyzed solvability conditions in Sobolev spaces

Abstract

For systems of ordinary differential equations on a compact interval, we study the character of solvability of the most general linear boundary-value problems in Sobolev spaces. We find the indices of these problems and obtain a criterion of their well-posedness.