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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 306917, 8 pages
Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument
1Department of Mathematics, Faculty of Arts and Science, Namik Kemal University, 59030 Tekirdağ, Turkey
2Department of Mathematics Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey
3Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea
4Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey
Received 18 November 2012; Accepted 1 March 2013
Academic Editor: Suh-Yuh Yang
Copyright © 2013 Erdoğan Şen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. Teschl, Ordinary Differential Equations and Dynamical Systems, vol. 140, American Mathematical Society, Providence, RI, USA, 2012.
- M. Shahriari, A. J. Akbarfam, and G. Teschl, “Uniqueness for inverse Sturm-Liouville problems with a finite number of transmission conditions,” Journal of Mathematical Analysis and Applications, vol. 395, no. 1, pp. 19–29, 2012.
- T. Kim, “Identities involving Frobenius-Euler polynomials arising from non-linear differential equations,” Journal of Number Theory, vol. 132, no. 12, pp. 2854–2865, 2012.
- S. B. Norkin, “On a boundary problem of Sturm-Liouville type for a second-order differential equation with a retarded argument,” Izvestija Vysših Učebnyh Zavedeniĭ Matematika, vol. 6, no. 7, pp. 203–214, 1958 (Russian).
- S. B. Norkin, Differential Equations of the Second Order with Retarded Argument, vol. 31 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1972.
- R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, London, UK, 1963.
- G. V. Demidenko and V. A. Likhoshvaĭ, “On differential equations with retarded argument,” Siberian Mathematical Journal, vol. 46, no. 3, pp. 417–430, 2005.
- G. V. Demidenko and I. I. Matveeva, “On numerical study of asymptotic stability of solutions to linear periodic differential equations with a parameter,” Journal of Computational Mathematics and Optimization, vol. 5, no. 3, pp. 163–173, 2009.
- A. Bayramov, S. Öztürk Uslu, and S. Aliskan, “Computation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument,” Applied Mathematics and Computation, vol. 191, no. 2, pp. 592–600, 2007.
- E. Şen, S. Araci, and M. Acikgoz, “Asymptotic behavior of eigenvalues and fundamental solutions of one discontinuous fourth-order boundary value problem,” Research Journal of Mathematical and Statistical Sciences, vol. 1, no. 1, pp. 23–32, 2013.
- E. Şen and S. Araci, “Computation of Eigenvalues and fundamental solutions of a fourth-order boundary value,” Proceedings of the Jangjeon Mathematical Society, vol. 15, no. 4, pp. 455–464, 2012.
- E. Şen and A. Bayramov, “On calculation of eigenvalues and eigenfunctions of a Sturm-Liouville type problem with retarded argument which contains a spectral parameter in the boundary condition,” Journal of Inequalities and Applications, vol. 2011, article 113, 2011.
- E. Şen and A. Bayramov, “On a discontinuous Sturm-Liouville type problem with retarded argument,” American Institute of Physics Conference Proceedings, vol. 1389, pp. 1172–1175, 2011.
- E. Şen and A. Bayramov, “Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the boundary condition,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 3090–3097, 2011.
- A. Bayramov and E. Şen, “On a Sturm-Liouville type problem with retarded argument,” Mathematical Methods in the Applied Sciences, vol. 36, no. 1, pp. 39–48, 2013.
- C. T. Fulton, “Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions,” Proceedings of the Royal Society of Edinburgh A, vol. 77, no. 3-4, pp. 293–308, 1977.
- P. A. Binding, P. J. Browne, and B. A. Watson, “Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter II,” Journal of Computational and Applied Mathematics, vol. 148, no. 1, pp. 147–168, 2002.
- N. Altinisik, M. Kadakal, and O. Sh. Mukhtarov, “Eigenvalues and eigenfunctions of discontinuous Sturm-Liouville problems with eigenparameter-dependent boundary conditions,” Acta Mathematica Hungarica, vol. 102, no. 1-2, pp. 159–175, 2004.
- N. B. Kerimov and Kh. R. Mamedov, “On a boundary value problem with a spectral parameter in the boundary conditions,” Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 40, no. 2, pp. 325–335, 1999.
- I. Titeux and Y. Yakubov, “Completeness of root functions for thermal conduction in a strip with piecewise continuous coefficients,” Mathematical Models & Methods in Applied Sciences, vol. 7, no. 7, pp. 1035–1050, 1997.