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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 503267, 7 pages
Green's Function Method for Self-Adjoint Realization of Boundary-Value Problems with Interior Singularities
Department of Mathematics, Faculty of Arts and Science, Gaziosmanpaşa University, 60250 Tokat, Turkey
Received 24 June 2013; Accepted 5 September 2013
Academic Editor: Ravshan Ashurov
Copyright © 2013 K. Aydemir and O. Sh. Mukhtarov. 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. Green, “An essay on the application of mathematical analysis to theories of electricity and magnetism,” The Journal für die Reine und Angewandte Mathematik, vol. 39, pp. 73–89, 1850.
- C. Neumann, Undersuchungen ber das Logaritmische and Newton'sche Potential, Teubner, Leipzig, Germany, 1877.
- E. W. Hobson, “Synthetical solutions in the conduction of heat,” Proceedings of the London Mathematical Society, vol. 19, no. 1, pp. 279–294, 1887.
- P. Appell, “Sur l'équation = 0 et la théorie de la chaleur,” Journal de Mathématiques Pures et Appliquées, vol. 8, pp. 187–216, 1892.
- G. Kirchhoff, “Zur Theorie der Lichtstrahlen,” Annalen der Physik, vol. 18, pp. 663–695, 1883.
- H. Burkhardt, “Sur les fonctions de Green relatives à un domaine d'une dimension,” Bulletin de la Société Mathématique de France, vol. 22, pp. 71–75, 1894.
- 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.
- A. V. Likov and Y. A. Mikhailov, The Heory of Heat and Mass Transfer, Qosenergaizdat, 1963.
- 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.
- J. Ao, J. Sun, and M. Zhang, “The finite spectrum of Sturm-Liouville problems with transmission conditions,” Applied Mathematics and Computation, vol. 218, no. 4, pp. 1166–1173, 2011.
- E. Bairamov and E. Uğurlu, “The determinants of dissipative Sturm-Liouville operators with transmission conditions,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 805–813, 2011.
- B. Chanane, “Sturm-Liouville problems with impulse effects,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 610–626, 2007.
- M. Kadakal and O. Sh. Mukhtarov, “Discontinuous Sturm-Liouville problems containing eigenparameter in the boundary conditions,” Acta Mathematica Sinica (English Series), vol. 22, no. 5, pp. 1519–1528, 2006.
- F. S. Muhtarov and K. Aydemir, “Distributions of eigenvalues for Sturm-Liouville problem under jump conditions,” Journal of New Results in Science, vol. 1, pp. 81–89, 2012.
- O. Sh. Mukhtarov and H. Demir, “Coerciveness of the discontinuous initial-boundary value problem for parabolic equations,” Israel Journal of Mathematics, vol. 114, pp. 239–252, 1999.
- O. Muhtarov and S. Yakubov, “Problems for ordinary differential equations with transmission conditions,” Applicable Analysis, vol. 81, no. 5, pp. 1033–1064, 2002.
- 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.
- A. Wang, J. Sun, X. Hao, and S. Yao, “Asymptotic behavior of a differential operator with discontinuities at two points,” Mathematical Methods in the Applied Sciences, vol. 34, pp. 373–383, 2011.
- E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations. Part I, Clarendon Press, Oxford, UK, 2nd edition, 1962.