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jzs-10737

Asymptotic Estimation of the Eigenvalues and Eigenfunctions for the Sixth Order Boundary Value Problems

 Karwan H. F. Jwamer1,  & Khelan. H. Qadr1

1Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, Kurdistan-Iraq


Abstract

This paper addresses an eigenvalue problem generated by sixth order differential equations with suitable boundary conditions, which contain a spectral parameter. The asymptotic expressions for sixth order linearly independent solutions as well as new asymptotic formulas for the eigenvalues with eigenfunctions of the boundary value problem are obtained.

Key Words: Eigenvalue problem, eigenfunction, spectral parameter, asymptotic formula

References

 

[1] H. Menken, "Accurate Asymptotic Formulas for Eigenvalues and Eigenfunctions of a Boundary-Value  Problem of Fourth Order", Hindawi Publishing Corporation, (2010).

 [2] K. H. Jwamer, K. H. Qadr, "Estimation of Normalized Eigen-functions of Spectral Problem with Smooth Coefficients", ACT A UNIVERSITATIS APULENSIS, (2010).

[3] K. H. Jwamer, R.Q.Rasul, "The Asymptotic Estimations of the Eigen-values and Eigenfunctions for the Fourth Order Boundary Value Problem with Smooth Coefficients", Math. Sci. Lett. Vol. 6, No. 2, pp. 121-129. (2017).

[4] K. H. Jwamer, R.Q.Rasul, "Estimations of the Upper Bound for the Eigen-Functions of the Fourth Order  Boundary Value Problem with Smooth Coefficients", Math. Sci. Lett. Vol. 6, No. 1, pp. 67-74. (2017)

[5] G. A. Aigunov, K. H. F. Jwamer, G. A. Dzhalaeva, "Estimates for the Eigenfunctions of the Regge  Problem". Published in Matematicheskie Zametki, Vol. 92, No. 1, pp. 141–144. (2012).       

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 [7] J. D. Tamarkin, "Some general problems of the theory of ordinary linear differential equations and  expansion of arbitrary functions in series Petrograd". (1917).    

 [8] M. A.Naimark, "Linear Differential Operators. Part 1". New York: Frederick Ungar, (1967). 

[9] Yu.Tamila, "Analysis of Spectral Characteristics of One Non-selfadjoint Problem with Smooth  Coefficients", South of Russian: PhD thesis, Dagestan State University, (2010).