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## Spectral problems for operators with deviating arguments

#### Milenko Pikula [1] , Elmir Čatrnja [2] , Ismet Kalčo [3]

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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.
Inverse problem with delays, Volterra integral equation, Fourier trigonometric coefficient, boundary spectral problems
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Primary Language en Mathematics Mathematics Author: Milenko PikulaInstitution: UNİVERSITY OF EAST SARAJEVOCountry: Bosnia and Herzegovina Author: Elmir Čatrnja (Primary Author)Institution: DZEMAL BIJEDIC UNIVERSITY OF MOSTARCountry: Bosnia and Herzegovina Author: Ismet KalčoInstitution: UNİVERSITY OF ZENICACountry: Bosnia and Herzegovina
 Bibtex @research article { hujms471105, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2018}, volume = {47}, pages = {1172 - 1183}, doi = {}, title = {Spectral problems for operators with deviating arguments}, key = {cite}, author = {Pikula, Milenko and Čatrnja, Elmir and Kalčo, Ismet} } APA Pikula, M , Čatrnja, E , Kalčo, I . (2018). Spectral problems for operators with deviating arguments. Hacettepe Journal of Mathematics and Statistics, 47 (5), 1172-1183. Retrieved from http://dergipark.gov.tr/hujms/issue/39860/471105 MLA Pikula, M , Čatrnja, E , Kalčo, I . "Spectral problems for operators with deviating arguments". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1172-1183 Chicago Pikula, M , Čatrnja, E , Kalčo, I . "Spectral problems for operators with deviating arguments". Hacettepe Journal of Mathematics and Statistics 47 (2018): 1172-1183 RIS TY - JOUR T1 - Spectral problems for operators with deviating arguments AU - Milenko Pikula , Elmir Čatrnja , Ismet Kalčo Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1172 EP - 1183 VL - 47 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Spectral problems for operators with deviating arguments %A Milenko Pikula , Elmir Čatrnja , Ismet Kalčo %T Spectral problems for operators with deviating arguments %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 5 %R %U ISNAD Pikula, Milenko , Čatrnja, Elmir , Kalčo, Ismet . "Spectral problems for operators with deviating arguments". Hacettepe Journal of Mathematics and Statistics 47 / 5 (October 2018): 1172-1183.