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Singüler Sturm-Liouville Problemi için Teklik Teoremi

A Uniqueness the Theorem for Singular Sturm-Liouville Problem

Journal Name:

  • Cumhuriyet Üniversitesi Fen Fakültesi Fen Bilimleri Dergisi

Publication Year:

  • 2003

Key Words:

Keywords (Original Language):

Author NameUniversity of Author
Abstract (2. Language): 
In this paper, we show that If q(x) is prescribed on the (%/2,ft] then the one spectrum suffices to determine q(x) on the interval (0, %/2) .The potential function q(x) in a Sturm Liouville problem is uniquely determined with one spectra by using the Hochstadt and Lieberman's method [2].
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Abstract (Original Language): 
Bu makalede gösterdi ki q(x) (%/2,T] aralığında tanımlanmış ise (0,7t/2) aralığı üzerinde q(x) fonksiyonunu belirlemek için bir spektrum yeterlidir. Sturm-Liouville probleminde q(x) potansiyel fonksiyonu Hochstadt ve Lieberman metodu kullanılarak bir spektruma göre tek olarak belirlenir.
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REFERENCES

References: 

1. Gasymov, M.G., The Definition of Sturm-Liouville Operator from Two Spectra, DAN SSSR, Vol.161, No:2, 1965, 274-276
2. Hochstadt , H. and Lieberman , B., An Invers Sturm Liouville Problem with Mixed Given Data. Siam J. Appl. Math. , Vol.34 , No: 4 , 1978, 676-680
3. Levitan, B.M., On the Determination of the Sturm - Liouville Operator from One and Two Spectra, Math. USSR Izvestija, vol. 12 , 1978, 179-193
4. Panakhov , E . S. , The definition of differential operator with peculiarity in zero on two spectrum. VINITI , N 4407 - 8091980 , 1980 , 1-16
5. Volk, V.Y., On Inverse Formulas for a Differential Equation with a Singularity at x=0, Usp.Mat.Nauk (N.S.) 8(56), 1953, 141-151
6. Watson, G., A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1962

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