Indefinite eigenvalue problems with several singular points and turning points

Citation
W. Eberhard et al., Indefinite eigenvalue problems with several singular points and turning points, MATH NACHR, 229, 2001, pp. 51-71
Citations number
25
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE NACHRICHTEN
ISSN journal
0025584X → ACNP
Volume
229
Year of publication
2001
Pages
51 - 71
Database
ISI
SICI code
0025-584X(2001)229:<51:IEPWSS>2.0.ZU;2-X
Abstract
We consider a general class of eigenvalue problems with two-point boundary conditions on a finite interval generated by a differential equation with a n indefinite weight function which has several zeros and/or poles. As a bas ic result we derive asymptotic estimates for a special fundamental system o f solutions of the corresponding differential equation and determine the as ymptotic distribution of the eigenvalues. Finally we prove the uniform conv ergence of eigenfunction expansions for some class of functions f.