The Journal of the Indian Mathematical Society

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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


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1 Department of Mathematics, Associate Professor in Mathematics (Retd.) Vivekananda College, Kolkata 700063, India
     

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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.

Keywords

Asymptotic Solutions, Turning Points, Dirichlet Boundary Conditions, Normalized Eigenvector.
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  • 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.

  • Klyuchnyk , I.H., Asymptotic solutions of a system of differential equations with multiple turning points, Ukranian Mathematical Journal, 61(11), Nov. (2009), 1780–1797.

  • 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.

  • 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.


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  • 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

Abstract Views: 200  |  PDF Views: 1

Authors

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

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.

Keywords


Asymptotic Solutions, Turning Points, Dirichlet Boundary Conditions, Normalized Eigenvector.

References