References:
[1] Berezanski.J.M,Expansion in Eigenfunctions of Selfadjoint Operators.,Transl.Math. Monographs 17, American Mathematical Soc, Providence,1968.
[2] Bicadze.A.V, Equations of mixed type.,M. Izd. AN SSSR,1959 (Russian).
[3] Burenko. V.V, Sobolev Spaces on Domains., Teubner, 1999.
[4] Dezin. A.A,Partial Differential Equations.(An Introduction to a General Theory of Linear Boundary Value Problems),Springer,1987.
[5] Fichera. G, On a unied theory of boundary value problems for elliptic-parabolic equations of second order., Boundary Problems of Differential Equations, The Univ. of Wisconsin Press,pp. 97-120 , 1960.
[6] Kalvand. Daryoush, Neumann problem for the degenerate differential-operator equations of the fourth order., Vestnik RAU, Physical-Mathematical and Natural Sciences, No. 2,pp. 34-41, 2010 (Russian).
[7] Kalvand. Daryoush, Tepoyan. L, Neumann problem for the fourth order degenerate ordinary differential equation., Proceedings of the Yerevan State University, Physical and Mathematical Sciences, No. 1,pp. 22-26, 2010.
[8] Kalvand. Daryoush, Tepoyan. L, Rashidinia. J, Existence and uniqueness of the fourth order boundary value problem and quintic Spline solution., Proceeding of 9th Seminar on Differential Equations and Dynamical Systems, 11-13 July, Iran,pp. 133-136, 2012.
[9] Keldi. M. V, Fis, On certain cases of degeneration of equations of elliptic type on the boundary of a domain., Dokl. Akad. Nauk. SSSR, 77,pp. 181-183, 1951 (Russian).
[10] Rashidinia,J.Direct methods for solution of a linear fourth-order two-point boundary value problem.,J. Intern.Eng.Sci., Vol.13,pp.37-48(2002).
[11] Rashidinia, J.Jalilian,R. Non-polynomial spline for solution of boundary value problems in plate defection theory., J. Comput. Math., 84(10), pp.1483-1494.(2007)
[12] Rashidinia,J.Mahmoodi,R.Jalilian,R.Quintic spline solution of Boundary value problem in plate Defection.,
J. Comput. Sci.Eng.,Vol.16,No.1,pp.53-59(2009).
[13] Romanko. V.K, On the theory of the operators of the form, Differential Equations,Vol. 3,No. 11, pp. 1957-1970, 1967 (Russian).
[14] Showalter. R.E, Hilbert Space Methods for Partial Differential Equations., Electronic Journal of Differential Equations, Monograph 01, 1994.
[15] Tepoyan. L, Degenerate fourth-order dierential-operator equations.,Differ. Urav, Vol. 23(8), 1987, pp. 1366- 1376, (Russian); English Transl. in Amer. Math. Soc.,No. 8, 1988.
[16] Tepoyan. L, On a degenerate dierential-operator equation of higher order., Izvestiya Natsionalnoi AkademiiNauk Armenii. Matematika, Vol.34(5), pp. 48-56,1999.
[17] Tepoyan. L, On the spectrum of a degenerate operator., Izvestiya Natsionalnoi Akademii Nauk Armenii. Matematika,Vol. 38,No. 5,pp. 53-57, 2003.
[18] Tepoyan. L, The Neumann problem for a degenerate dierential-operator equation., Bulletin of TICMI (Tbil-isi International Centre of Mathematics and Informatics),Vol. 14, pp. 1-9, 2010.
[19] Tricomi, F, On linear partial dierential equations of second order of mixed type., M., Gostexizdat, 1947 (Russian).
254 J. Rashidinia et al. / J. Linear. Topological. Algebra. 02(04) (2013) 243-254.
[20] Usmani,R.A. Discrete methods for boundary value problems with applications in plate defection the-
ory.,J.Appl.Math.Phys., 30 ,pp.87-99(1979).
[21] Visik. M.I, Boundary-value problems for elliptic equations degenerate on the boundary of a region., Mat. Sb.,
35(77), pp. 513-568,1954 (Russian); Amer. Math. Soc,Vol. 35,No. 2,(English) 1964.
[22] Zahra ,W.K,Ashraf, M.El,Mhlawy. Numerical solution of two-parameter singularly perturbed boundary vproblems via exponential spline, Journal of King Saudi University Science January(2013).