Author:
Thakar Sarita,Demanna Pratiksha
Abstract
Multiplicity of eigenvalues of the regular indefinite Sturm- Liouville problem ?y"" + qy = ?wy on [a, b] subject to periodic boundary conditions is discussed. A necessary and sufficient condition for the existence of non-simple real eigenvalues is proved. Eigenfunctions corresponding to non-simple real eigenvalues are obtained. In this article, we discuss the interlacing property in one turning point case with periodic boundary conditions.
Publisher
Informatics Publishing Limited
Reference15 articles.
1. A. L. Andrew, Correction of finite difference eigenvalues of periodic Sturm-Liouville problems, ANZIAM J., 30(4) (1989), 460–469.
2. F. V. Atkinson and D. Jabon, Indefinite Sturm-Liouville problems, in Proc. 1984 Workshop on Spectral Theory of Sturm-Liouville Differential Operators, Argonne National Laboratory, Reprint ANL-84-73, 31–46.
3. J. Behrndt, F. Philipp, C. Trunk, Bounds on the non-real spectrum of differential operators with indefinite weights, Mathematische Annalen., 357(1) (2013), 185–213.
4. ?I. C¸ elik, G. Gokmen, Approximate solution of periodic Sturm-Liouville problems with Chebyshev collocation method, Appl. Math. Comput., 170(1) (2005), 285–295.
5. E. L. Ince, Ordinary Differential Equations, Dover Publications, INC. New York, 1956.