ASYMPTOTIC BEHAVIORS OF THE SOLUTION AND EIGENVALUES OF SPECTRAL PROBLEM.  Karwan H.F, Jwamer  Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Iraq.
 Hawsar Ali  Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Iraq.
 ABSTRACT

In this paper, we study the asymptotic behaviors of the solutions and eigenvalues of the differential equations of fourth order with boundary conditions are proposed and analyzed.

Asymptotic Behaviors, eigenvalues, solutions, spectral problem, boundary conditions.

[1] Gadzhieva, T. Yu., “Analysis of spectral characteristics of one non-self adjoinproblem with smooth coefficients”, PhD thesis, Dagestan State University, South of Russian, [2010]. 261

[2] Karwan H.F. Jwamer and Aryan A.M, “Study the Behavior of the Solution and Asymptotic Behaviors of Eigenvalues of a Six Order Boundary Value Problem”,International Journal of Research and Reviews in Applied Sciences, Vol.13, Issue 3, December 2012,p.790-799, Pakistan.

[3] Karwan H.F. Jwamer and Aryan A.M, “Boundedness of Normalized Eigenfunctions of the Spectral Problem in the Case of Weight Function Satisfying the Lipschitz Condition”, Journal of ZankoySulaimani – Part A [JZS-A], Vol. 15, No.1, 2013,p.79-94.

[4] Karwan .H.F.Jwamer ,Aigounv G.A and GajivaT.Yu, “The study of the asymptotic behavior of the eigenvalues and the estimate for the kernel of the resolvent of an irregular boundary value problem generated by a differential equation of order four on the interval [0, a]”, Bulletin of Dagestan State University, Natural Sciences , Makhachkala[South of Russian], Vol.4,No.4 ,2007,p. 93-97.

[5] Karwan H.F.Jwamer, Hawsar Ali HR, “Asymptotic Behaviors of the Eigenvalues and Solution of a Fourth Order Boundary Value Problem”, International Journal of Partial Differential Equations and Applications, Vol.3, No.2, 2015, p.25-28.

[6] Naimark .M.A, “Linear Differential Operators”, New York, USA, 1968.

[7] Shkalikov A.A, “Boundary value problem with a spectral parameter in the boundary Conditions”, Zeitchrift fur AngewandteMathematikund Mechanik, Vol.76, pp.133- 135, 1996.

[8] Tamarkin.Ya.D, “About some general problems of theory of ordinary linear Differential equations and about decomposition of arbitrary functions in series”, Petrograd 1917.

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