References
- S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and H. Holden (2005). Solvable Models in Quantum Mechanics, 2nd ed. AMS Chelsea Publishing, Providence, RI.
- J. Ao, J. Sun, and M. Zhang (2012). Matrix representations of Sturm–Liouville problems with transmission conditions. Comput. Math. Appl. 63:1335–1348.
- K. Aydemir and O. Sh. Mukhtarov (2013). Green’s function method for self-adjoint realization of boundary-value problems with interior singularities. Abstr. Appl. Anal. 2013: Article ID 503267, 7 pages.
- D. Hinton and P. W. Schaefer (1997). Spectral Theory and Computational Methods for Sturm–Liouville Problems. Lecture Notes in Pure and Applied Mathematics, vol. 191, Marcel Dekker Inc., New York.
- M. Kandemir (2010). Irregular boundary value problems for elliptic differential-operator equations with discontinuous coefficients and transmission conditions. Kuwait J. Sci. Eng. 39(1A):71–97.
- M. Kandemir and O. Mukhtarov (2000). Asymptotic behavior of eigenvalues of the functional-many point boundary-value problem with discontinuous coefficients. Bull. Pure Appl. Sci. 19(2):373–384.
- Q. Kong and Q. Wang (2013). Using time scales to study multi-interval Sturm–Liouville problems with interface conditions. Results. Math. 63:451–465.
- B. M. Levitan and I. S. Sargsyan (1991). Sturm–Liouville and Dirac Operators. Springer-Verlag, New York.
- A. V. Likov and Yu. A. Mikhailov (1963). The Theory of Heat and Mass Transfer. Qosenergaizdat, Russian.
- O. Sh. Mukhtarov and H. Demir (1999). Coersiveness of the discontinuous initial- boundary value problem for parabolic equations. Israel J. Math. 114:239–252.
- O. Sh. Mukhtarov and M. Kadakal (2005). Some spectral properties of one Sturm–Liouville type problem with discontinuous weight. Sib. Math. J. 46:681–694.
- O. Sh. Mukhtarov and S. Yakubov (2002). Problems for ordinary differential equations with transmission conditions. Appl. Anal. 81:1033–1064.
- O. Sh. Mukhtarov, H. Olğar, and K. Aydemir (2014). Transmission problems for Sturm–Liouville equation involving an abstract linear operator. AIP Conf. Proc. 1611:325.
- J. D. Pryce (1993). Numerical Solution of Sturm–Liouville Problems. Monographs on Numerical Analysis. The Clarendon Press Oxford University Press, New York (Oxford Science Publications).
- M. L. Rasulov (1967). Methods of Contour Integration. North-Holland Publishing Company, Amsterdam.
- A. N. Tikhonov and A. A. Samarskii (1963). Equations of Mathematical Physics. Oxford, New York, Pergamon.
- E. C. Titchmarsh (1962). Eigenfunctions Expansion Associated with Second Order Differential Equations I. Oxford University Press, London.
- I. Titeux and Ya. Yakubov (1997). Completeness of root functions for thermal conduction in a strip with piecewise continuous coefficients. Math. Models Methods Appl. Sci. 7(7):1035–1050.
- E. Uǧurlu and E. Bairamov (2013). Dissipative operators with impulsive conditions. Math. Chem. 51:1670–1680.
- N. N. Voitovich, B. Z. Katsenelbaum, and A. N. Sivov (1997). Generalized Method of Eigen-vibration in the Theory of Diffraction. Nauka, Moscow(Russian).