INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT

Yıl 2015, Cilt: 36 Sayı: 5, 113 - 133, 28.04.2015

Rauf Amirov , Sevim Durak

https://doi.org/10.17776/csj.43222

Öz

In this paper,the Sturm-Liouville with discontinuous coe¢ cient
is considered. ·Integral equations for solution which satisfy certain initial of
given and equation has been obtained and useful integral representation for
Sturm-Liouville operator.

Anahtar Kelimeler

Integral equation, Sturm-Liouville, kernel

Kaynakça

• V.A. Ambartsumyan, Über eine Frage der Eigenwerttheorie, Z. Physik 53 (1929), 690-695.
• G.Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimnungder Dif- ferentialgleichung durch die Eigenwerte, Acta Math. 78 (1945), 1-96.
• N. Levinson, 1949, The Inverse Sturm-Liouville Problem, Mat. Tidsskr. B., pp. 25-30.
• B. M. Levitan, 1964, Generalized Translation Operators and some of its Applications, Jerusalem.
• V.A. Marchenko, Some Problems in the Theory of Second-order DiferentialOperators, Dokl. Akad., Nauk SSSR. 72 (1950), 457-560.
• I. M. Gelfand and B. M. Levitan, 1951 On Determination of a Di¤erentialEquation by its
• Spectral Function Izv. Akad. Nauk SSSR Ser. Mat. 15 309-60 (in Russian). M.G. Gasimov and B. M. Levitan, About Sturm-Liouville Di¤erential. Operators., Math. Sborn., 63 (105), No. 3, (1964).
• A.N. Tikhonov, Uniqueness Theorems for Jeophysics Problems, Dokl. Akad. Nauk. SSSR, Vol 69, No 4, 1949, 797-800.
• R. O. Hryniv and Ya. V. Mykytyuk, Inverse Spectral Problems for Sturm- Liouville Operators with Singular Potentials, Inverse Problems 19 (2003) 665-684.
• A. M. Savchuk and A. A. Shkalikov, 1999 Sturm-Liouville Operators with Singular Potentials
• Mat. Zametki 66 897-912 (in Russian). V. A. Marchenko 1950 Some Questions of the Theory of Second Order Dixoerential Operators
• Dokl. Akad. Nauk SSSR 72 457-60. O. Hald, 1984 Discontinuous Inverse Eigenvalue Problem Commun. Pure Appl. Math. 37 539
• R. Carlson, 1994 Inverse Sturm-Liouville Problems with a Singularity at Zero Inverse Prob- lems 10 851-64.
• V. A. Yurko, 2000 Inverse Problems for Di¤erential Equations with Singularities Lying Inside the Interval J. Inverse III-Posed Probl. 8 89-103.
• R. Kh. Amirov and V. A. Yurko, On Di¤erential Operators with Singularity and Discontinuity Conditions Inside the Interval. Ukr. Math. Jour., 2001, v.53, No11, p. 1443-1458.
• R. Kh. Amirov, Transformation Operators for Strum-Liouville Operators with Singular Po- tentials, Int. Journal of Pure and Applied Math., 12(3), (2004).
• R. Kh Amirov, Direct and Inverse Problems for Di¤erential Operators with Singularity and Discontinuity Conditions Inside the Interval Transactions of NASAzerbaijan. R. Kh Amirov, On Sturm-Liouville Operators with Discontinuity Conditions Inside an Inter- val J. Math. Anal. Appl. 317 (2006) 163-176.
• Nilifer Topsakal, Sonlu Aralıkta Coulomb Potansiyele Sahip Sturm- Liouville Operatörü Için Ters ( Inverse) Problemler (2008)
• S. Albeverio and P. Kurasov, 2000 Singular Perturbations of Di¤erential Operators, Solvable
• Schrödinger Type Operators (Cambridge: Cambridge University Press) J. Pöschel and E. Trubowitz, 1987 Inverse Spectral Theory(Pure Appl. Math. Vol 130)(Or- lando, FL:Academic).