Electron. J. Diff. Equ., Vol. 2016 (2016), No. 131, pp. 1-14.

Asymptotic distribution of eigenvalues and eigenfunctions for a multi-point discontinuous Sturm-Liouville problem

Kadriye Aydemir, Oktay Sh. Mukhtarov

In this article we study a class of generalized BVP' s consisting of discontinuous Sturm-Liouville equation on finite number disjoint intervals, with usual boundary conditions and supplementary transmission conditions at finite number interior points. The asymptotic behaviors of the eigenvalues and eigenfunctions are discussed. By modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we find asymptotic formulas for the eigenvalues and eigenfunctions.

Submitted February 20, 2016. Published June 6, 2016.
Math Subject Classifications: 34B24, 34L20.
Key Words: Sturm-Liouville problems; eigenvalue; eigenfunction; asymptotic distribution.

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Kadriye Aydemir
Faculty of Education
Giresun University
28100 Giresun, Turkey
email: kadriyeaydemr@gmail.com
Oktay Sh. Mukhtarov
Department of Mathematics
Faculty of Arts and Science
Gaziosmanpasa University
60250 Tokat, Turkey
email: omukhtarov@yahoo.com

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