Vol2 Paper 22

posted Aug 27, 2018, 12:25 AM by Yaseen Raouf Mohammed   [ updated Sep 4, 2018, 2:16 AM ]

 Aryan Ali Mohammed

 Department of Mathematics, College of Science, University of Sulaimani, Sulaimanyah,Iraq.

In this paper, we solve a type of the spectral linear ordinary differential equation of second order with two different types of coefficients. First type of coefficients are some real polynomials of the independent variable, while the second type of the coefficients are real valued continuous functions of the independent variable, and each of these two types are reduced to the constant coefficients by changing the independent variable to new variable. Examples have been included to show the usefulness and effectiveness of our technique.

Change of variable; real polynomials; spectral parameter; general solution; variationof parameters.

[1] Arficho, D. [2015], Method for Solving Particular Solution of Linear Second Order Ordinary Differential Equations, J Appl Computat Math 4(2), 1-3.
[2] Bellman, R. [1953], Stability Theory of Differential Equations, McGraw-Hill, New York.
[3] Cesari, L. [1963], Asymptotic Behavior and Stability Problems in Ordinary DifferentialEquations, Springer-Verlag, Berlin.
[4] Coppel, W. A. [1965], Stability and Asymptotic Behavior of Differential Equations, Heat, Boston, Mass.
[5] Coppel, W. A. [1971], Disconjugacy, Springer-Verlag, Berlin.
[6] Gadzhieva, T. Yu. [2010], Analysis of spectral characteristics of one nonself adjoint problem with smooth coefficients, PhD thesis, Dagestan State University, South of Russian.
[7] Hartman, P. and Wintner, A. [1949], On the Laplace-Fourier transcendent, Amer. J. Math 71, 367-372.
[8] Hartman, P. [1964], Ordinary Differential Equations, Wiley, New York.
[9] Hochtadt, H. [1964], on the stability of certain second-order differential equations, Sot. Ind.Appl. Math 12, 58-59.
[10] Johnson, P., Busawon, K. and Barbot, J. [2008], Alternative solution of the inhomo-geneous linear differential equation of order two, J. Math. Anal. Appl 339, 582–589.
[11] Jwamer, K. H. and Mohammed, A. A. [2013], Boundedness of Normalized Eigenfunctions of the Spectral Problem in the Case of Weight Function Satisfying the Lipschitz Condition,
Journal of Zankoy Sulaimani – Part A 15(1), 79-94.
[12] Jwamer, K. H. and Mohammed, A. A. [2012], 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 13(3), 790-799.
[13] Marini, M. [1975], Criteri di limitatezza per le soluzioni dell’equazione lineare de1 second ordine, Boll. U.M.I 4, 154-165.
[14] Marini, M. and Zezza, P. [1978], On the Asymptotic Behavior of the Solutions of a Classof Second-Order Linear Differential Equations, Journal of Differential Equations 28,1-17.
[15] Mohammed, A. A. [2016], Eigenfunctions and asymptotic behavior of Eigenvalues to the given boundary value problem with Eigenparameter in the boundary conditions, Journal of Zankoy Sulaimani – Part A 18(1), 179-190.
[16] Moore, R. A. [1955], The behavior of solutions of a linear differential equation of secondorder, Pacific J. Math 5, 125-145. 247
[17] Nemytskii, V. V and Stepanov, V. V. [1960], Qualitative Theory of Differential Equations, Princeton Univ. Press, Princeton, New Jersey.
[18] Richard, U. [1964], Serie asintotiche per una classe di equazioni differenziali non oscillanti de1 second ordine, Uniw. Polit. Torino, Rend. Sent. Mat 23, 171-217.
[19] Sansone, G. [1941], Equazioni Differenziali Nel Campo Reale II, Zanichelli, Bologna.
[20] Swanson, C. A. [1968], Comparison and Oscillatory Theory of Linear Differential Equations, Academic Press, New York.

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