Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T06:02:48.079Z Has data issue: false hasContentIssue false
  • English
  • Français

STURM–LIOUVILLE PROBLEMS WITH DISCONTINUOUS POTENTIAL

Part of: Ordinary differential operators

Published online by Cambridge University Press:  01 June 2008

Z. AKDOĞAN  and
Z. ŞAŞMAZ
Z. AKDOĞAN*
Affiliation:
Gaziosmanpasa University, Faculty of Science-Art, Department of Mathematics, 60240 Tokat, Turkey (email: [email protected])
Z. ŞAŞMAZ
Affiliation:
Şehit Vural Arıcı Anadolu Lisesi, 06920 Nallıhan/Ankara, Turkey (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider a discontinuous Sturm–Liouville equation together with two supplementary transmission conditions at the point of discontinuity. We suggest our own approach for finding asymptotic approximation formulas for the eigenvalues of such discontinuous problems.

Keywords

Sturm–Liouville problemstransmission conditionsasymptotic of eigenvalues and eigenfunctionsdiscontinuous boundary-value problems

MSC classification

Secondary: 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 485 - 494
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Binding, P. A. and Browne, P. J., ‘Oscillation theory for indefinite Sturm–Liouville problems with eigenparameter dependent boundary conditions’, Proc. Roy. Soc. Edinburgh Sect. A 127(6) (1997), 1123–1136.CrossRefGoogle Scholar
[2]Fulton, C. T., ‘Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions’, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 293–308.CrossRefGoogle Scholar
[3]Shkalikov, A. A., ‘Boundary value problems for ordinary differential equations with a parameter in boundary conditions’, Tr. Semin. im. I. G. Petrovskogo 9 (1983), 190–229.Google Scholar
[4]Kerimov, N. B. and Memedov, Kh. K., ‘On a boundary value problem with a spectral parameter in the boundary conditions’, Sibirsk. Mat. Zh. 40(2) (1999), 325–335 (English translation: Siberian Math. J. 40(2) (1999), 281–290).Google Scholar
[5]Kobayashi, M., ‘Eigenvalues of discontinuous Sturm–Liouville problems with symmetric potentials’, Comput. Math. Appl. 18(4) (1989), 357–364.CrossRefGoogle Scholar
[6]Likov, A. V. and Mikhailov, Yu. A., The Theory of Heat and Mass Transfer (Qosenergoizdat, 1963), (in Russian).Google Scholar
[7]Mukhtarov, O. Sh., Kandemir, M. and Kuruoğlu, N., ‘Distribution of eigenvalues for the discontinunous boundary value problem with functional many point conditions’, Israel J. Math. 129 (2002), 143–156.CrossRefGoogle Scholar
[8]Mukhtarov, O. Sh. and Kandemir, M., ‘Asymptotic behaviour of eigenvalues for the discontinuous boundary-value problem with functional-transmission conditions’, Acta Math. Sci. B 22(3) (2002), 335–345.CrossRefGoogle Scholar
[9]Mukhtarov, O. Sh., Kadalak, M. and Altınışık, N., ‘Eigenvalues and eigenfunctions of discontinuous Sturm–Liouville problems with eigenparameter in the boundary conditions’, Indian J. Pure Appl. Math. 34(3) (2003).Google Scholar
[10]Mukhtarov, O. Sh. and Yakubov, S., ‘Problems for ordinary differential equations with transmission conditions’, Appl. Anal. 81 (2002), 1033–1064.CrossRefGoogle Scholar
[11]Rasulov, M. L., Methods of Contour Integratian (North-Holland, Amsterdam, 1967).Google Scholar
[12]Titchmarsh, E. C., Eigenfunction Expansions Associated with Second Order Differential Equations I, 2nd edn (Oxford University Press, London, 1962).CrossRefGoogle Scholar
[13]Yakubov, S. and Yakubov, Y., ‘Abel basis of root functions of regular boundary value problems’, Math. Nachr. 197 (1999), 157–187.CrossRefGoogle Scholar