## Journal of Applied Mathematics

### Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument

#### Abstract

In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. This is the first work containing two discontinuities points in the theory of differential equations with retarded argument. In that special case the transmission coefficients $\delta =\gamma =\mathrm{1}$ and retarded argument $\mathrm{\Delta }\equiv \mathrm{0}$ in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 306917, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807936

Digital Object Identifier
doi:10.1155/2013/306917

Mathematical Reviews number (MathSciNet)
MR3039753

Zentralblatt MATH identifier
1266.34041

#### Citation

Şen, Erdoğan; Seo, Jong Jin; Araci, Serkan. Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument. J. Appl. Math. 2013 (2013), Article ID 306917, 8 pages. doi:10.1155/2013/306917. https://projecteuclid.org/euclid.jam/1394807936

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