This article is cited in 20 papers

Brief communications

A Sturm–Liouville Inverse Spectral Problem with Boundary Conditions Depending on the Spectral Parameter

C. Van der Mee^a, V. N. Pyvovarchyk<sup>b

a</sup> Università di Cagliari
^b Odessa State Academy of Building and Architecture

Abstract: We consider a boundary value problem generated by the Sturm-Liouville equation on a finite interval. Both the equation and the boundary conditions depend quadratically on the spectral parameter. This boundary value problem occurs in the theory of small vibrations of a damped string. The inverse problem, i.e., the problem of recovering the equation and the boundary conditions from the given spectrum, is solved.

Keywords: Sturm–Liouville problem, damped string, spectral parameter-dependent boundary conditions, eigenvalues, asymptotics.

UDC: 517.43+517.9

Received: 10.12.2001

DOI: 10.4213/faa222

 English version: Functional Analysis and Its Applications, 2002, 36:4, 315–317

Bibliographic databases:

• 
• 
• 
•