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Study of the eigenvalues of Sturm-Liouville problems under perturbations
Corresponding Author(s) : OCTAVIA-MARIA HAPENCIUC
Student Thinkers and Advanced Research,
Vol. 3 No. 1 (2024): Proceedings of the 7th International Conference XGEN
Abstract
This research paper aims to investigate how the eigenvalues of Sturm-Liouville problems behave when the differential equation or coefficients are subjected to perturbations. Specifically, the study seeks to examine the continuity of eigenvalues concerning these perturbations.
The research involves theoretical analysis, numerical simulations using Python and MATLAB programming languages, and potential development of new mathematical techniques to characterize the behavior of eigenvalues.
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- A. Zettl, "Sturm-Liouville Problems", Mathematics Department, Northern Illinois University, DeKalb, Illinois 60115. E. A. Coddington and A. Zettl, Hermitian and anti-Hermitian properties of Green’s matrices., Pacific J. Math. 18 (1966), 451-454.
- J. W. Neuberger, “Concerning boundary value problems", Pacific J. Math. 10 (1960), 1385-1392. A. Zettl, Adjoint and self-adjoint problems with interface conditions., SIAM J. Applied Math. 16, (1968), 851-859.
- M. S. Robertson, "Ad jointness in nonadjoint boundary value problems", SIAM J. Applied Math. 17, (1969), 1268-1279.
- Q. Kong and A. Zettl, "Linear ordinary differential equations", WSSIAA v.3, (1994), (Special volume dedicated to Walter), Inequalities and Applications, edited by R. P. Agarwal, 381- 397.
- J. Weidmann, "Linear Operators in Hilbert Spaces", volume 68 of Graduate Texts in Mathematics. Springer Verlag, Berlin, 1980.
- P. Kosowski, "A Simple Proof Of The Spectral Continuity Of The Sturm–Liouville Problem", Symplicit Singularities And Geometry Of Gauge Fields, Banach Center Publications, Volume 39, Institute Of Mathematics, Polish Academy Of Sciences, Warszawa 1997.
- R. Courant and D. Hilbert, "Methods of Mathematical Physics", vol. 1, Intercedence, New York, 1953.
- P. Kosowski, "A Note on The Relative Error for The Eigenvalues Of The Sturm-Liouville Problem", Demonstration Mathematica, Vol. XXXII No 2 1999.
References
A. Zettl, "Sturm-Liouville Problems", Mathematics Department, Northern Illinois University, DeKalb, Illinois 60115. E. A. Coddington and A. Zettl, Hermitian and anti-Hermitian properties of Green’s matrices., Pacific J. Math. 18 (1966), 451-454.
J. W. Neuberger, “Concerning boundary value problems", Pacific J. Math. 10 (1960), 1385-1392. A. Zettl, Adjoint and self-adjoint problems with interface conditions., SIAM J. Applied Math. 16, (1968), 851-859.
M. S. Robertson, "Ad jointness in nonadjoint boundary value problems", SIAM J. Applied Math. 17, (1969), 1268-1279.
Q. Kong and A. Zettl, "Linear ordinary differential equations", WSSIAA v.3, (1994), (Special volume dedicated to Walter), Inequalities and Applications, edited by R. P. Agarwal, 381- 397.
J. Weidmann, "Linear Operators in Hilbert Spaces", volume 68 of Graduate Texts in Mathematics. Springer Verlag, Berlin, 1980.
P. Kosowski, "A Simple Proof Of The Spectral Continuity Of The Sturm–Liouville Problem", Symplicit Singularities And Geometry Of Gauge Fields, Banach Center Publications, Volume 39, Institute Of Mathematics, Polish Academy Of Sciences, Warszawa 1997.
R. Courant and D. Hilbert, "Methods of Mathematical Physics", vol. 1, Intercedence, New York, 1953.
P. Kosowski, "A Note on The Relative Error for The Eigenvalues Of The Sturm-Liouville Problem", Demonstration Mathematica, Vol. XXXII No 2 1999.