Distributions of eigenvalues for Sturm-Liouville problem under jump conditions

F. S. Muhtarov; Kadriye Aydemir; Kadriye Aydemir

Year 2012, Volume: 1 Issue: 1, 81 - 89, 01.01.2012

F. S. Muhtarov Kadriye Aydemir Kadriye Aydemir

Abstract

References

Z. Akdo˘gan, M. Demirci and O. Sh. Mukhtarov, Green function of discontinuous boundary value problem with Transmissions conditions, Math. Meth. Appl. Sci. 30(2007)1719-1738.
B. Chanane, Eigenvalues of Sturm-Liouville problems with discontinuity conditions inside a finite interval, Appl. Math. Comput. 188(2007), 1725-1732.
C. T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edin. 77A(1977), 293-308.
M. Kadakal and O. Sh. Mukhtarov, Discontinuous Sturm-Liouville Problems Containing Eigenparameter in the Boundary Conditions. Acta Mathematica Sinica, English Series Sep., 22(5)(2006), pp. 1519-1528.
M. Kandemir, O. Sh. Mukhtarov and Y.Y. Yakubov , Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter, Mediterr, J. Math. 6(2009), 317-338.
O. Sh. Mukhtarov, M. Kadakal and F. S. Muhtarov On discontinuous Sturm-Liouville Problems with transmission conditions. J. Math. Kyoto Univ., Vol. 44, No. 4( 2004), 779-798.
J. D. Pryce, Numeric Solution of SturmLiouville Problems Clarendon, Oxford, 1993.
E. C. Titchmarsh Eigenfunctions Expansion Associated with Second Order Differential Equations I, second edn. Oxford Univ. Press, London, (1962).
A Wang, J. Sun and A. Zettl, Two-interval SturmLiouville operators in modified Hilbert spaces, J. Math. Anal. Appl., 328(2007), 390-399.
A. Zettl, Adjoint and self-adjoint boundary value problems with interface conditions SIAM J. Appl. Math. 16 (1968) 851-859.

Distributions of eigenvalues for Sturm-Liouville problem under jump conditions

Year 2012, Volume: 1 Issue: 1, 81 - 89, 01.01.2012

F. S. Muhtarov Kadriye Aydemir Kadriye Aydemir

Abstract

This paper deals with the asymptotic estimates of eigenvalues for SturmLiouville problems with two supplementary transmission conditions at one interior point. By modifying some known techniques the existence and uniqueness results of solutions are obtained for the considered problem

Keywords

Sturm-Liouville problems, transmission conditions, eigenvalue, eigenfunction

References

Z. Akdo˘gan, M. Demirci and O. Sh. Mukhtarov, Green function of discontinuous boundary value problem with Transmissions conditions, Math. Meth. Appl. Sci. 30(2007)1719-1738.
B. Chanane, Eigenvalues of Sturm-Liouville problems with discontinuity conditions inside a finite interval, Appl. Math. Comput. 188(2007), 1725-1732.
C. T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edin. 77A(1977), 293-308.
M. Kadakal and O. Sh. Mukhtarov, Discontinuous Sturm-Liouville Problems Containing Eigenparameter in the Boundary Conditions. Acta Mathematica Sinica, English Series Sep., 22(5)(2006), pp. 1519-1528.
M. Kandemir, O. Sh. Mukhtarov and Y.Y. Yakubov , Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter, Mediterr, J. Math. 6(2009), 317-338.
O. Sh. Mukhtarov, M. Kadakal and F. S. Muhtarov On discontinuous Sturm-Liouville Problems with transmission conditions. J. Math. Kyoto Univ., Vol. 44, No. 4( 2004), 779-798.
J. D. Pryce, Numeric Solution of SturmLiouville Problems Clarendon, Oxford, 1993.
E. C. Titchmarsh Eigenfunctions Expansion Associated with Second Order Differential Equations I, second edn. Oxford Univ. Press, London, (1962).
A Wang, J. Sun and A. Zettl, Two-interval SturmLiouville operators in modified Hilbert spaces, J. Math. Anal. Appl., 328(2007), 390-399.
A. Zettl, Adjoint and self-adjoint boundary value problems with interface conditions SIAM J. Appl. Math. 16 (1968) 851-859.

There are 10 citations in total.

Details

Primary Language	English
Journal Section	Articles
Authors	F. S. Muhtarov This is me Kadriye Aydemir This is me Kadriye Aydemir This is me
Publication Date	January 1, 2012
Published in Issue	Year 2012 Volume: 1 Issue: 1

Cite

APA	Muhtarov, F. S., Aydemir, K., & Aydemir, K. (2012). Distributions of eigenvalues for Sturm-Liouville problem under jump conditions. Journal of New Results in Science, 1(1), 81-89.
AMA	Muhtarov FS, Aydemir K, Aydemir K. Distributions of eigenvalues for Sturm-Liouville problem under jump conditions. JNRS. January 2012;1(1):81-89.
Chicago	Muhtarov, F. S., Kadriye Aydemir, and Kadriye Aydemir. “Distributions of Eigenvalues for Sturm-Liouville Problem under Jump Conditions”. Journal of New Results in Science 1, no. 1 (January 2012): 81-89.
EndNote	Muhtarov FS, Aydemir K, Aydemir K (January 1, 2012) Distributions of eigenvalues for Sturm-Liouville problem under jump conditions. Journal of New Results in Science 1 1 81–89.
IEEE	F. S. Muhtarov, K. Aydemir, and K. Aydemir, “Distributions of eigenvalues for Sturm-Liouville problem under jump conditions”, JNRS, vol. 1, no. 1, pp. 81–89, 2012.
ISNAD	Muhtarov, F. S. et al. “Distributions of Eigenvalues for Sturm-Liouville Problem under Jump Conditions”. Journal of New Results in Science 1/1 (January 2012), 81-89.
JAMA	Muhtarov FS, Aydemir K, Aydemir K. Distributions of eigenvalues for Sturm-Liouville problem under jump conditions. JNRS. 2012;1:81–89.
MLA	Muhtarov, F. S. et al. “Distributions of Eigenvalues for Sturm-Liouville Problem under Jump Conditions”. Journal of New Results in Science, vol. 1, no. 1, 2012, pp. 81-89.
Vancouver	Muhtarov FS, Aydemir K, Aydemir K. Distributions of eigenvalues for Sturm-Liouville problem under jump conditions. JNRS. 2012;1(1):81-9.

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