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

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  • Erdoğan Şen
  • Jong Jin Seo
  • Serkan Araci

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 and retarded argument in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

Suggested Citation

  • Erdoğan Şen & Jong Jin Seo & Serkan Araci, 2013. "Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, April.
    • Handle: RePEc:hin:jnljam:306917
    DOI: 10.1155/2013/306917
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