This article is cited in 35 papers

On the Eigenvalues and Eigenfunctions of the Sturm–Liouville Operator with a Singular Potential

A. M. Savchuk

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper we consider the Sturm–Liouville operators generated by the differential expression $-y+q(x)y$ and by Dirichlet boundary conditions on the closed interval $[0,\pi]$. Here $q(x)$ is a distribution of first order, i.e., $\int q(x)dx\in L_2[0,\pi]$. Asymptotic formulas for the eigenvalues and eigenfunctions of such operators which depend on the smoothness degree of $q(x)$ are obtained.

UDC: 517.9+517.43

Received: 29.05.2000
Revised: 05.07.2000

DOI: 10.4213/mzm502

 English version: Mathematical Notes, 2001, 69:2, 245–252

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