BİR SÜREKSİZ STURM-LIOUVILLE PROBLEMİNİN GREEN FONKSİYONU, RESOLVENT OPERATÖRÜ VE KENDİNE EŞLENİKLİĞİ

Yıl 2012, Cilt: 5 Sayı: 1, 85 - 102, 12.03.2014

Mahir Kadakal F. Ş. Muhtarov Nihat Altınışık

Öz

Bu makalede, sınır şartlarının her ikisinde özdeğer parametresi bulunduran bir süreksiz Sturm-Liouville probleminin bazı spektral özellikleri incelenmiştir. Problemin Green fonksiyonu ve resolvent operatörü bulunmuş, ayrıca kendine-eşlenikliği ispatlanmıştır.

Anahtar Kelimeler

Sturm-Liouville problemi, Green fonksiyonu, Resolvent operatörü

Kaynakça

• Akdoğan, Z., Demirci, M., and Mukhtarov, O. Sh. (2007). Green function of discontinuous boundary-value problem with transmission conditions, Mathematical methods in the applied Sciences, Math. Meth. Appl. Sci. 30, 1719–1738.
• Binding, P. A., Browne, P. J. and Watson, B. A., (1997). Oscillation theory for indefinite Sturm-Liouville problems with boundary conditions rationallay dependent on the eigenparameter, II, J. Comput. Appl. Math. 148, 147- 168.
• Binding, P. A., Browne, P. J. and Watson, B. A., (2002). Sturm-Liouville problems with eigenparameter dependent boundary conditions, Proc. Royal Soc. Edinburg, 127A, 1123-1136. Appl. Math. 148, 147-168.
• Boumenir, A. (2005). Sampling the miss-distance and transmission function. Journal of Mathematical Analysis and Applications, 310 (1), 197-208.
• Fulton, C. T. (1977). Two Point Boundary Value Problems with Eigenvalue Parameter Contained in the Boundary Conditions. Proc. Soc. Edinburg, 77A, p.293–308. Hinton,D.
• (1979). An Expansion Theorem for in Eigenvalue problem
• with Eigenvalue Parameter in the Boundary Condition. Quarterly
• Journal of Mathematics, Oxf. (2), 30, 33–42.
• Lang, S. (1983). Real Analysis (Second edition), Addision-Wesley, Reading, Mass.
• Mukhtarov, O. Sh., (1994). Discontinuous boundary-value problem with spectral parameter in boundary conditions. Turkish Journal of Mathematics, 18, pp. 183-192.
• Mukhtarov, O. S., Kadakal, M. and Altinisik, N., (2003). Eigenvalues and eigenfunctions of discontinuous Sturm-Liouville problems with eigenparameter in the boundary conditions, Indian Journal of Pure and Applied Mathematics, 34(3) 501–516.
• Mukhtarov O. Sh. and Tunç E., (2004). Eigenvalue problems for Sturm-Liouville equations with transmission conditions, Israel Journal of Mathematics, 144, 367-380.
• Mukhtarov, O. Sh., Kadakal, M. and Muhtarov, F. S. (2004). On Discontinuous Sturm-Liouville Problems with Transmission Conditions, J. Math. Kyoto Univ., 44(4), 779-798.
• Naimark, M.A. (1967). Linear Differential Operators, Ungar, New York.
• Schneider, A. (1974). A note on Eigenvalue Problems with Eigenvalue Parameter in the Boundary Condition. Mathematische Zeitschrift, Z.136, 163–167.
• Shkalikov, A.A. (1983). Boundary Value Problems for Ordinary Differential Equations with a Parameter in Boundary Condition. Trudy. Sem., Imeny, I.G. Petrosgo, 9, 190-229. Titchmarsh, E.C.
• (1939). Eigenfunction Expansion Associated with Second
• Order Differential Equations I., (2nd end). Oxford University Press, London.
• Tunç E., and Muhtarov, O.SH., (2004). Fundamental Solutions And Eigenvalues of One Boundary-Value Problem with Transmission Conditions, Applied Mathematics and Computation, 157, 347–355
• Walter, J. (1973). Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions. Mathematische Zeitschrift Z. 133, 301– 312.
• Wang Guixia, Sun Jiong, (2008). Properties of Eigenvalues of A Class of Discontinuous Sturm-Liouville Problems, Journal of Inner Mongolia Normal Univ., Vol: 37, No: 3.
• Boyce, W. E. and DiPrima, R.C.(2001).Elementary Differential Equations and Boundary Value Problems, 7th ed. John Wiley & Sons, Inc. Yakubov, S.
• & Yakubov, Y. (2000). Differential-Operator Equations.
• Ordinary and Partial Differential Equations, Chapman and Hall//CRC (Boca Raton).
• Yang Q. and Wanyi W. (2010). A Discontinuous Sturm-Liouville Operator With Indefinite Weight, Journal of Mathematics Research, 2(3), 161-168.
• Yang, Qiuxia, (2011). Asymptotic behavior of a differential operator with discontinuities at two points. Mathematical methods in the Applied Sciences, 34,4, 373-383 Mar 15.
• Zayed, E.M.E. & Ibrahim, S.F.M. (1992). Regular Eigenvalue Problem with Eigenparameter in the Boundary Conditions. Bulletin of Calcutta Mathematical Society, 84. 379–393. ****