An expansion result for a Sturm-Liouville eigenvalue problem with impulse

FAYDAOĞLU, ŞERİFE; GUSEINOV, Gusein Sh.

An expansion result for a Sturm-Liouville eigenvalue problem with impulse

ŞERİFE FAYDAOĞLU, (Dokuz Eylül Üniversitesi, İzmir, Türkiye)

Gusein Sh. GUSEINOV (Atılım Üniversitesi, Ankara, Türkiye)

Turkish Journal of Mathematics

3 0

Yıl: 2010 Cilt: 34 Sayı: 3 Sayfa Aralığı: 355 - 366 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

An expansion result for a Sturm-Liouville eigenvalue problem with impulse

Öz:

The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Amirov, R. Kh.: On Sturm-Liouville operators with discontinuity conditions inside an interval, J. Math. Anal. Appl., 317, 163–176 (2006).
[2] Bainov, D. D. and Simeonov, P. P.: Impulsive Differential Equations: Asymptotic Properties of the Solutions, World Scientific, Singapore, 1995.
[3] Bainov, D. D. and Simeonov, P. P.: Oscillation Theory of Impulsive Differential Equations, International Publication, Florida, 1998.
[4] Chanane, B.: Eigenvalues of Sturm-Liouville problems with discontinuity conditions inside a finite interval, Appl. Math. Comput., 188, 1725–1732 (2007).
[5] Chanane, B.: Sturm-Liouville problems with impulse effects, Appl. Math. Comput., 190, 610–626 (2007).
[6] Churchill, R. V.: Operational Mathematics, 3rd ed., McGraw-Hill, New York, 1972.
[7] Faydaoglu, S. and Guseinov, G. Sh.: Eigenfunction expansion for a Sturm-Liouville boundary value problem with impulse, International Journal of Pure and Applied Mathematics, 8, 137–170 (2003).
[8] Guseinov, G. Sh.: Eigenfunction expansions for a Sturm-Liouville problem on time scales, International Jornal of Difference Equations, 2, 93–104 (2007).
[9] Kolmogorov, A. N. and Fomin, S. V.: Introductory Real Analysis, Prentice-Hall, Englewood Cliffs, 1970.
[10] Lakshmikantham, V., Bainov, D.D. and Simeonov, P. S.: Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
[11] Mukhtarov, O. Sh., Kadakal, M. and Muhtarov, F. S¸.: Eigenvalues and normalized eigenfunctions of discontinuous Sturm-Liouville problem with transmission conditions, Rep. Math. Phys., 54, 41–56 (2004).
[12] Muhtarov, O. and Yakubov, S.: Problems for ordinary differential equations with transmission conditions, Appl. Anal., 81, 1033–1064 (2002).
[13] Ozisik, M. N.: Boundary Value Problems of Heat Conduction, Dower, New York, 1989.
[14] Samoilenko, A. M. and Perestyuk, N. A.: Impulsive Differential Equations, World Scientific, Singapore, 1995.
[15] Smirnov, V. I.: A Course of Higher Mathematics, Vol. IV, Addison-Wesley, New York, 1964.
[16] Wang, A., Sun, J. and Gao, P.: Completeness of eigenfunctions of Sturm-Liouville problems with transmission conditions, J. Spectral Math. Appl., Vol. 2006, 10pp. (electronic).

APA	FAYDAOĞLU Ş, GUSEINOV G (2010). An expansion result for a Sturm-Liouville eigenvalue problem with impulse. , 355 - 366.
Chicago	FAYDAOĞLU ŞERİFE,GUSEINOV Gusein Sh. An expansion result for a Sturm-Liouville eigenvalue problem with impulse. (2010): 355 - 366.
MLA	FAYDAOĞLU ŞERİFE,GUSEINOV Gusein Sh. An expansion result for a Sturm-Liouville eigenvalue problem with impulse. , 2010, ss.355 - 366.
AMA	FAYDAOĞLU Ş,GUSEINOV G An expansion result for a Sturm-Liouville eigenvalue problem with impulse. . 2010; 355 - 366.
Vancouver	FAYDAOĞLU Ş,GUSEINOV G An expansion result for a Sturm-Liouville eigenvalue problem with impulse. . 2010; 355 - 366.
IEEE	FAYDAOĞLU Ş,GUSEINOV G "An expansion result for a Sturm-Liouville eigenvalue problem with impulse." , ss.355 - 366, 2010.
ISNAD	FAYDAOĞLU, ŞERİFE - GUSEINOV, Gusein Sh.. "An expansion result for a Sturm-Liouville eigenvalue problem with impulse". (2010), 355-366.

APA	FAYDAOĞLU Ş, GUSEINOV G (2010). An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics, 34(3), 355 - 366.
Chicago	FAYDAOĞLU ŞERİFE,GUSEINOV Gusein Sh. An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics 34, no.3 (2010): 355 - 366.
MLA	FAYDAOĞLU ŞERİFE,GUSEINOV Gusein Sh. An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics, vol.34, no.3, 2010, ss.355 - 366.
AMA	FAYDAOĞLU Ş,GUSEINOV G An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics. 2010; 34(3): 355 - 366.
Vancouver	FAYDAOĞLU Ş,GUSEINOV G An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics. 2010; 34(3): 355 - 366.
IEEE	FAYDAOĞLU Ş,GUSEINOV G "An expansion result for a Sturm-Liouville eigenvalue problem with impulse." Turkish Journal of Mathematics, 34, ss.355 - 366, 2010.
ISNAD	FAYDAOĞLU, ŞERİFE - GUSEINOV, Gusein Sh.. "An expansion result for a Sturm-Liouville eigenvalue problem with impulse". Turkish Journal of Mathematics 34/3 (2010), 355-366.