Прегледај по Аутор "Čatrnja, Elmir"

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    Spectral problems for operators with deviating arguments
    (Faculty of Science and Mathematics, University of Hacettepe, 2018) Pikula, Milenko; Čatrnja, Elmir; Kalčo, Ismet
    The topic of this paper are direct and inverse spectral boundary problems of the Sturm-Liouville type with two deviating arguments, one delay and one advance. This type of problem was firstly introduced by M. Pikula, E. Čatrnja, I. Kalčo and A. Šarić at the 9th International Scientific Conference "Science and Higher Education in Function of Sustainable Development - SED 2016" and further developed M. Pikula, E. Čatrnja, I. Kalčo at the International Conference "Contemporary Problems of Mathematical Physics and Computational Mathematics" dedicated to the 110th anniversary of A. N. Tikhonov. In this paper we take both delays to have the same value and in its first part solve the direct boundary problem, construct the corresponding characteristic function and find the asymptotic behavior of eigenvalues. In the second part of the paper, we give the necessary and sufficient conditions for the existence of the solution of the inverse problem and give its solution by the method of Fourier coefficients.
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    Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay
    (2022) Nedić, Dragana; Čatrnja, Elmir
    In this paper we observe the operator D2 = D2(h,H, q, ), h,H 2 R = R [ {−1,1}, q(x) 2 L2 [0, ], 2 (0, 1) and construct and partially transform its characteristic function. Those transformations enable more complete asymptotic decomposition of the zeroes and eigenvalues of the operator. The goal of this paper is to contribute to the development of the spectral theory of differ-ential operators with homogeneous delay.