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

Abstract

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.

Keywords

• Sturm-Liouville problemi, Green fonksiyonu, Resolvent operatörü

References

1. 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.
2. 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.
3. 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.
4. Boumenir, A. (2005). Sampling the miss-distance and transmission function. Journal of Mathematical Analysis and Applications, 310 (1), 197-208.
5. 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.
6. (1979). An Expansion Theorem for in Eigenvalue problem
7. with Eigenvalue Parameter in the Boundary Condition. Quarterly
8. Journal of Mathematics, Oxf. (2), 30, 33–42.

9. Lang, S. (1983). Real Analysis (Second edition), Addision-Wesley, Reading, Mass.
10. Mukhtarov, O. Sh., (1994). Discontinuous boundary-value problem with spectral parameter in boundary conditions. Turkish Journal of Mathematics, 18, pp. 183-192.
11. 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.
12. Mukhtarov O. Sh. and Tunç E., (2004). Eigenvalue problems for Sturm-Liouville equations with transmission conditions, Israel Journal of Mathematics, 144, 367-380.
13. 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.
14. Naimark, M.A. (1967). Linear Differential Operators, Ungar, New York.
15. Schneider, A. (1974). A note on Eigenvalue Problems with Eigenvalue Parameter in the Boundary Condition. Mathematische Zeitschrift, Z.136, 163–167.
16. 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.
17. (1939). Eigenfunction Expansion Associated with Second
18. Order Differential Equations I., (2nd end). Oxford University Press, London.
19. 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
20. Walter, J. (1973). Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions. Mathematische Zeitschrift Z. 133, 301– 312.
21. 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.
22. Boyce, W. E. and DiPrima, R.C.(2001).Elementary Differential Equations and Boundary Value Problems, 7th ed. John Wiley & Sons, Inc. Yakubov, S.
23. & Yakubov, Y. (2000). Differential-Operator Equations.
24. Ordinary and Partial Differential Equations, Chapman and Hall//CRC (Boca Raton).
25. Yang Q. and Wanyi W. (2010). A Discontinuous Sturm-Liouville Operator With Indefinite Weight, Journal of Mathematics Research, 2(3), 161-168.
26. 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.
27. 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. ****