Sturm-Liouville problems with impulse effects

Applied Mathematics and Computation

Volumn 190, Issue 1, 2007, Pages 610-626

  Chanane, B ^a  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Discontinuous Sturm Liouville problems; Impulsive Sturm Liouville problems; Interface conditions; Regularized sampling method; Shannon's sampling theory; Transmission conditions; Whittaker Shannon Kotel'nikov theorem

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; IMPULSE RESPONSE;

DISCONTINUOUS STURM-LIOUVILLE PROBLEMS; IMPULSIVE STURM-LIOUVILLE PROBLEMS; INTERFACE CONDITIONS; REGULARIZED SAMPLING METHOD; SHANNON'S SAMPLING THEORY; TRANSMISSION CONDITIONS; WHITTAKER-SHANNON-KOTEL'NIKOV THEOREM;

PROBLEM SOLVING;

EID: 34249813725     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.01.092     Document Type: Article

References (18)

1. M.U. Akhmet, O. Ugur, The Sturm-Liouville operator on the space of functions with discontinuity conditions.
2. Amirov R.Kh. On Sturm-Liouville operators with discontinuity conditions inside an interval. J. Math. Anal. Appl. 317 (2006) 163-176
3. Boumenir A., and Chanane B. Eigenvalues of S-L systems using sampling theory. Appl. Anal. 62 (1996) 323-334
4. B. Chanane, Eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.11.082.
5. Chanane B. Computation of the eigenvalues of Sturm-Liouville Problems with parameter dependent boundary conditions using the regularized sampling method. Math. Comput. 74 252 (2005) 1793-1801 (published electronically S 0025-5718(05)01717-5 (2005))
6. Chanane B. High order approximations of the eigenvalues of Sturm-Liouville problems with coupled self-adjoint boundary conditions. Appl. Anal. 80 (2001) 317-330
7. Chanane B. High order approximations of the eigenvalues of regular Sturm-Liouville problems. J. Math. Anal. Appl. 226 (1998) 121-129
8. Dunford N., and Schwartz J.T. Linear Operators, Part III (1971), Wiley-Interscience, New York
9. Edmunds E.E., and Evans W.D. Spectral Theory and Differential Operators (1987), Clarendon/Oxford University Press, New York
10. Hinton D., and Schaefer P.W. Spectral Theory and Computational Methods of Sturm-Liouville Problems (1997), Marcel Dekker, Inc.
11. O.Sh. Mukhtarov, Mahir Kadakal, Eigenvalues and normalized eigenfunctions of discontinuous Sturm-Liouville problem with transmission conditions, Rep. Math. Phys., 54 (1), 41-56.
12. Mukhtarov O.Sh., and Yakubov S. Problems for differential equations with transmission conditions. Appl. Anal. 81 (2002) 1033-1064
13. Titeux I., and Yakubov S. Completeness of root functions for thermal conduction in a strip with piecewise continuous coefficients. Math. Mod. Meth. Appl. Sci. 7 (1997) 1035-1050
14. M.A. Naimark, Linear Differential Operators, Part I, Ungar, 1968.
15. Pryce J.D. Numerical Solution of Sturm-Liouville Problems (1993), Oxford Science Publications, Clarendon Press
16. Wang A., Sun J., and Gao P. Completeness of eigenfunctions of Sturm-Liouville problems with transmission conditions. J. Spectral Math. Appl. 1 (2005)
17. Zayed A.I. Advances in Shannon's Sampling Theory (1993), CRC Press
18. Zettl A. Adjoint and self-adjoint boundary value problems with interface conditions. SIAM J. Appl. Math. 16 (1968) 851-859