The Asymptotic Laws of the Distribution of Eigenvalues for a System of Second Order Differential Equations having Turning Points at Both Ends of the Interval

Jump To References Section

Authors

  • Debasish Sengupta
     Department of Mathematics, Associate Professor in Mathematics (Retd.), Vivekananda College, Kolkata 700063 ,IN

DOI:

https://doi.org/10.18311/jims/2023/26380

Keywords:

Asymptotic Solutions, Turning Points, Dirichlet Boundary Conditions, Normalized Eigenvector.
ordinary differential equation

Abstract

The paper deals with the asymptotic expressions for the solutions along with their first derivatives, the distribution of the eigenvalues and the normalized eigenvector for large eigenvalues corresponding to a system of second order differential equations having turning points at both ends of the interval, under certain suitable boundary conditions.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2023-03-24

How to Cite

Sengupta, D. (2023). The Asymptotic Laws of the Distribution of Eigenvalues for a System of Second Order Differential Equations having Turning Points at Both Ends of the Interval. The Journal of the Indian Mathematical Society, 90(1-2), 13–22. https://doi.org/10.18311/jims/2023/26380

Issue

Volume 90, Issue 1-2, January-June 2023

Section

Articles

License

Copyright (c) 2023 Debasish Sengupta

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC
Received 2020-11-12
Accepted 2021-11-14
Published 2023-03-24

 

References

Chakraborty, N.K. and Acharyya, S.K., On the distribution of eigenvalues of a differential system, Jour. Pure Math., 2 (1982), 71–90.

Chakraborty, N.K. and Acharyya, S.K., On an inverse problem involving a second order differential system, J. Indian Insc. Sci., May-June, (1991), 239–258.

Dorodnicyn, A.A., Asymptotic laws of distribution of the characteristic values for certain special forms of differential equations of the second order, Amer. Math. Soc. Transl., 16, No. 2 (1960), 1–101. DOI: https://doi.org/10.1090/trans2/016/01

Klyuchnyk , I.H., Asymptotic solutions of a system of differential equations with multiple turning points, Ukranian Mathematical Journal, 61(11), Nov. (2009), 1780–1797. DOI: https://doi.org/10.1007/s11253-010-0312-z

Langer, R.E., The asymptotic solution of ordinary linear differential equation of the second order with special reference to a turning point. Amer. Math. Soc., 67 (1949), 161–190. DOI: https://doi.org/10.1090/S0002-9947-1949-0033420-2

Naimark, M.A., Linear Differential Operators, Frederick Ungar Pub. Co. NY., 1967.

Sengupta, D., Asymptotic expressions for the eigenvalues and eigenvectors of a system of second order differential equations with a turning point. International Journal of Pure and Applied Mathematics, 62, No. 4 (2010), 381–398.

Sengupta, D., Asymptotic expressions for the eigenvalues and eigenvectors of a system of second order differential equations with a turning point (Extension-I). International Journal of Pure and Applied Mathematics, 72, No. 4 (2011), 453–462.

Sengupta, D., Asymptotic expressions for the eigenvalues and eigenvectors of a system of second order differential equations with a turning point (Extension-II), International Journal of Pure and Applied Mathematics, 78, No. 1 (2012), 85–95.

Wang, Na, Simple singular perturbation problems with turning points. Journal of Applied Mathematics and Physics, Vol. 7, No. 12, (2019), 2979–2989. DOI: https://doi.org/10.4236/jamp.2019.712208