A non-standard multiparameter eigenvalue problem in ordinary differential equations

✍ Scribed by M. Faierman; R. Mennicken

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 172 KB
• Volume: 278
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200410321

✦ Synopsis

Abstract

We consider two simultaneous Sturm–Liouville systems involving three spectral parameters. However unlike the standard multiparameter problem, we now suppose that the principal part of each of the differential operators involved is multiplied by a different parameter. For such a non‐standard system we establish the oscillation theory and discuss the associated eigenfunction expansion. Some open problems concerning the eigenfunction expansion are also presented. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)