YALÇIN GÜLDÜ
(Department of Mathematics, Faculty of Science, Cumhuriyet University 58140 Sivas, Turkey)
A. Sinan OZKAN
(Department of Mathematics, Faculty of Science, Cumhuriyet University 58140 Sivas, Turkey)
Yıl: 2017Cilt: 38Sayı: 2ISSN: 1300-1949 / 1300-1949Sayfa Aralığı: 204 - 218Türkçe

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Herglotz-Nevanlinna Fonksiyonu İçeren Sınır Koşullarına Sahip Dirac Operatörü için Ters Problemler
Bu makalede, sınır koşulları spektral parametreye rasyonel, süreksizlik koşulları ise lineer şekilde bağlı olan Dirac operatörü için ters problem ele alınmıştır. (½,1) aralığında Q(x) potansiyel fonksiyonu biliniyorken, tek spektrumun sonlu sayıda özdeğerlerin dışında (0,1) aralığında Q(x) potansiyel fonksiyonunu ve problemin diğer katsayılarını tek olarak belirlediği ispatlanmaktadır. Ayrıca, Q(x) fonksiyonunun klasik spektral veriler, yani özdeğerler ve normalleştirici sayılar yardımıyla tek olarak belirlendiği gösterilmektedir.
DergiAraştırma MakalesiErişime Açık
  • [1]. R.Kh. Amirov, A.S. Ozkan and B. Keskin, Inverse problems for impulsive Sturm-Liouville operator with spectral parameter linearly contained in boundary conditions, Integral Transforms and Special Functions, 20(8)(2009), 607-618.
  • [2]. R. Kh. Amirov, B. Keskin, A. S. Ozkan, Direct and inverse problems for the Dirac operator with spectral parameter linearly contained in boundary condition, Ukrainian Math. J., 61(91)(2009), 1155-1166.
  • [3]. T. N. Arutyunyan, Isospectral Dirac operators, Izv. Nats. Akad. Nauk Armenii Mat. 29(2)(1994), 3-14, ; English transl. in J. Contemp. Math. Anal., Armen. Acad. Sci. 29(2)(1994), 1-10.
  • [4]. P.A. Binding, P.J. Browne and K. Seddighi, Sturm-Liouville problems with eigenparameter dependent boundary conditions, Proc. Edinburgh Math. Soc., 37(2)(1993), 57-72.
  • [5]. P.A. Binding, P.J. Browne and B.A. Watson, Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions, J. London Math. Soc., 62(2000), 161-182.
  • [6]. P.A. Binding, P.J. Browne and B.A. Watson,. Equivalence of inverse Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, J. Math. Anal. Appl., 291(2004), 246-261.
  • [7]. P.A. Binding, P.J. Browne, B.A. Watson, Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, I, Proc.Edinburgh Math.Soc., 45(2002), 631-645.
  • [8]. P.A. Binding, P.J. Browne, B.A. Watson, Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, II, Journal of Computational and Applied Mathematics, 148(2002), 147-168.
  • [9]. P.J. Browne and B.D. Sleeman, A uniqueness theorem for inverse eigenparameter dependent Sturm-Liouville problems, Inverse Problems, 13(1997), 1453-1462.
  • [10]. Chernozhukova and G. Freiling, A uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditions, Inverse Problems in Science and Engineering, 17(6)(2009), 777-785.
  • [11]. G. Freiling and V.A. Yurko, Inverse Sturm-Liouville problems and their applications, Nova Science, New York, 2001.
  • [12]. G. Freiling and V.A. Yurko, Inverse problems for Sturm-Liouville equations with boundary conditions polynomially dependent on the spectral parameter, Inverse Problems, 26(2010) 055003 (17pp.).
  • [13]. C.T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. R. Soc. Edinburgh, A77(1977), 293-308.
  • [14]. M. G. Gasymov, Inverse problem of the scattering theory for Dirac system of order 2n, Tr. Mosk Mat. Obshch., 19(1968), 41-112, Birkhauser, Basel, (1997).
  • [15]. M. G. Gasymov and T. T. Dzhabiev, Determination of a system of Dirac differential equations using two spectra, Proceeding of School-Seminar on the Spectral Theory of Operators and Representations of Group Theory [in Russian], Elm, Baku, (1975), 46-71.
  • [16]. F. Gesztesy and B. Simon . Inverse spectral analysis with partial information on the potential II: The case of discrete spectrum. Trans. Amer. Math. Soc. 352(6)(2000), 2765-2787.
  • [17]. N.J. Guliyev, Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary condition, Inverse Problems, 21(2005), 1315-1330.
  • [18]. M. Guseinov, On the representation of Jost solutions of a system of Dirac differential equations with discontinuous coefficients, Izv. Akad. Nauk Azerb. SSR, 5(1999), 41-45.
  • [19]. Y. Güldü, A Half-Inverse Problem for Impulsive Dirac Operator with Discontinuous Coefficient, Abstract and Applied Analysis, Volume 2013, Article ID 181809.
  • [20]. O.H. Hald, Discontiuous inverse eigenvalue problems, Comm. Pure Appl. Math., 37(1984), 539- 577.
  • [21]. H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math. 34(1978), 676-680.
  • [22]. B. Keskin and A.S. Ozkan, Inverse spectral problems for Dirac operator with eigenvalue dependent boundary and jump conditions, Acta Math. Hungar., 130(4)(2011), 309-320.
  • [23]. B. Keskin, Inverse spectral problems for impulsive Dirac operators with spectral parameters contained in the boundary and discontinuity conditions polynomially, Neural Computing and Applications, 23(5)(2013), 1329-1333.
  • [24]. B.M. Levitan, and I. S. Sargsyan, Sturm-Liouville and Dirac operators [in Russian], Nauka, Moscow, 1988.
  • [25]. M.M. Malamud, Uniqueness questions in inverse problems for systems of differential equations on a finite interval, Trans. Moscow Math. Soc. 60(1999), 204-262.
  • [26]. R. Mennicken, H. Schmid and A.A. Shkalikov, On the eigenvalue accumulation of SturmLiouville problems depending nonlinearly on the spectral parameter, Math. Nachr., 189(1998), 157-170.
  • [27]. A.S. Ozkan, Half-inverse Sturm-Liouville problem with boundary and discontinuity conditions dependent on the spectral parameter, Inverse Problems in Science and Engineering 22(5)(2014), 848-859.
  • [28]. L. Sakhnovich, Half inverse problems on the finite interval. Inverse Problems 17(2001), 527-532.
  • [29]. H. Schmid and C. Tretter, Singular Dirac systems and Sturm-Liouville problems nonlinear in the spectral parameter, Journal of Differential Equations, 181(2)(2002), 511-542.
  • [30]. A.A. Shkalikov, Boundary value problems for ordinary differential equations with a parameter in the boundary conditions. J. Sov. Math. 33(1986), 1311-1342. Translation from Tr. Semin. Im. I.G. Petrovskogo 9(1983), 190-229.
  • [31]. C-Fu Yang and Z-You Huang, A half-inverse problem with eigenparameter dependent boundary conditions, Numerical Functional Analysis and Optimization, 31(6)(2010), 754-762.
  • [32]. C-Fu Yang, Hochstadt-Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions, Nonlinear Analysis Series A: Theory, Methods and Applications, 74(2011), 2475-2484.
  • [33]. C-Fu Yang, Determination of Dirac operator with eigenparameter dependent boundary conditions from interior spectral data, Inverse Problems in Science and Engineering, 20(3)(2012), 351-369.
  • [34]. V.A. Yurko, Boundary value problems with a parameter in the boundary conditions, Izv. Akad. Nauk Armyan. SSR, Ser. Mat., 19(5)(1984), 398-409. English translation in Soviet J. Contemporary Math. Anal., 19(5)(1984), 62-73.
  • [35]. V.A. Yurko, An inverse problem for pencils of differential operators, Mat Sbornik,191(10) (2000), 137-158 (Russian). English translation in Sbornik Mathematics, 191(2000), 1561-1586.
  • [36]. J. Walter, Regular eigenvalue problems with eigenvalue parameter in the boundary conditions. Math. Z. 133(1973), 301-312.

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