Affiliation:
1. SİVAS CUMHURİYET ÜNİVERSİTESİ
Abstract
In this paper, we construct the new integral representation of the Jost solution of Sturm-Liouville equation with impuls in the semi axis $[0,+\infty )$ and we give this type of relation, examine the properties of the Kernel function and their partial derivatives with $x$ and $\ t$, constructed integral representation and obtain the partial differential equation provided by this Kernel function. Finally, in the paper we prove uniqueness of the determination of the potential by the scattering data.
Publisher
Turkish Journal of Mathematics and Computer Science, Association of Mathematicians
Reference27 articles.
1. Agranovich, Z.S., Marchenko, V.A., The lnverse Problem of Scaterring Theory, New York: Gordonand Breach, 1963.
2. Agranovich, Z.S., Marchenko, V.A., Sturm Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977, English transl.: Birkhauser, 1986.
3. Akhmedova, E.N., Huseynov, H.M., On inverse problem Sturm-Liouville operator with discontinuous coefficients, Izvestiya of Saratov University. Mathematics Mechanics Informatics, 10(1)(2010), 3–9.
4. Amirov, R.Kh., On Sturm-Liouville operators with discontinuity conditions inside an interval, J. Math. Anal. Appl. 317(1)(2006), 163–176.
5. Faydaoğlu, S¸ ., Guseinov, G.Sh., An expansion result for a Sturm-Liouville eigenvalue problem with impulse, Turkish Journal of Mathematics, 34(3)(2010), 355–366.