Approximate Calculation of Eigenvalues and Eigenfunctions of
One Discontinuous Boundary Value Problem
[email protected], [email protected], [email protected]
Gaziosmanpaşa University, Tokat,
In this paper is considered a new boundary value problem consisting of eigen
parameter-dependent boundary and transmission conditions at interior points, as well as at the
end points of the interval. Our goal is to establish asymptotic formulae (with an arbitrary
number of terms) for the eigenvalues and eigenfunctions. In particular we find asymptotic
formulas for the eigenvalues and eigenfunctions.
Keywords. Boundary value problem, eigenvalue, eigenfunction, asymptotics of
eigenvalues and eigenfunction.
AMS 2010. 34B24, 34L15
[1] K. Aydemir and O. Sh. Mukhtarov Green's Function Method for Self-Adjoint Realization
of Boundary-Value Problems with Interior Singularities, Abstract and Applied Analysis, vol.
2013, Article ID 503267, 7pages, 2013. doi:10.1155/2013/503267.
[2] Mukhtarov, O. Sh. and Yakubov S., Problems for Ordinary Differential Equations with
Transmission Conditions, Applicaple Analysis, 81, 1033-1064, 2002.
[3] Titchmars, E. C., Eigenfunctions Expansion Associated with Second Order Differential
Equations I, second edn. Oxford Univ. press, London , 1962.
[4] Zettl, A., Adjoint and Self-adjoint Boundary Value Problems with Interface Conditions,
SIAM J. Appl. Math. 16, 851-859, 1968.
[5] Woldegerima , W.
The Sturm-Liouville Boundary Value Problems and their
applications: First Edition, LAP Lambert Academic Publishing, 2011 .

Approximate Calculation of Eigenvalues and Eigenfunctions of One