Abstract and Applied Analysis
Volume 2004 (2004), Issue 2, Pages 165-182
doi:10.1155/S1085337504310055

Spectral analysis for differential operators with singularities

Abstract

Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigen- and associated functions, and investigate the inverse problem of recovering the boundary value problem from its spectral characteristics.