Mathematician from the University of Banja Luka (Bosnia-Herzegovina) Solved a Decades-Long Inverse problem of the Sturm-Liouville-type with delay

Source #1: https://www.sciencedirect.com/science/article/abs/pii/S0893965920304377

Source #2 (Publication): https://www.researchgate.net/publication/344159679_On_an_open_question_in_recovering_Sturm-Liouville-type_operators_with_delay

Source #3 (News article from University of Banja Luka): https://www.unibl.org/en/news/2020/10/mathematician-from-the-university-of-banja-luka-solved-a-decades-long-problem

Mathematician from the University of Banja Luka Solved a Decades-Long Problem

Nebojša Đurić, Senior Assistant Mathematician at the Faculty of Architecture, Civil Engineering and Geodesy of the University of Banja Luka, managed to solve an over 40-year-old mathematical problem.

In the last decade, the area titled Inverse problem of the Sturm-Liouville-type with constant delay has expanded greatly, and the best mathematicians worldwide in this field have tried to give an answer to the open question: “Is there a unique solution to the inverse problem of the Sturm-Liouville-type with delay in the interval from π/3 to 2π/5 in the general case?”.

Many of them based their scientific research on the assumption that there was a unique solution. Despite the beliefs of the best mathematicians in the world, Nebojša Đurić gave a negative answer with a counterexample.

This result was published on 28 October 2020 in the journal ,,Applied Mathematics Letters’’, in the paper ,,On an open question in recovering Sturm-Liouville-type operators with delay”.

Đurić published the paper together with the Russian mathematician Sergey Buterin, who supported the idea of a counterexample.

The inverse problems of differential operators have significant applications in astrophysics, aerodynamics, and biophysics. Applied Mathematics Letters is one of the best journals on the SCI list in this field.

Nebojša Đurić is a scholarship holder of the Ministry of Scientific and Technological Development, Higher Education and Information Society of the Republic of Srpska. It was the Ministry that supported this research as part of the project titled "Phase Space Localization: Theoretical, Computational and Practical Aspects".

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