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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2025, Volume 239, Pages 25–31
DOI: https://doi.org/10.36535/2782-4438-2025-239-25-31 (Mi into1335) 		 
Necessary conditions for a minimum in variational problems with delay in the presence of degeneracie

M. J. Mardanovab, T. K. Melikovbac

a Baku State University
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
c Institute of Control Systems, National Academy of Sciences of Azerbaijan, Baku
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DOI: https://doi.org/10.36535/2782-4438-2025-239-25-31
Abstract: This article examines the minimum of an extremal in the variational problem with delay under the degeneracy of the Weierstrass condition. We obtain necessary conditions of equality type and inequality type for a strong as well as for a weak local minimum. Necessary conditions of equality and inequality types are obtained for strong as well as weak local minimum. A specific example demonstrating the effectiveness of the results in this paper is provided.
Keywords: variational problem with delayed argument, strong (weak) local minimum, necessary condition type equality (inequality), degeneration at the point
Document Type: Article
UDC: 517.972
MSC: 49Kxx
Language: Russian
Citation: M. J. Mardanov, T. K. Melikov, “Necessary conditions for a minimum in variational problems with delay in the presence of degeneracie”, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 239, VINITI, Moscow, 2025, 25–31
Citation in format AMSBIB
\Bibitem{MarMel25}
\by M.~J.~Mardanov, T.~K.~Melikov
\paper Necessary conditions for a minimum in variational problems with delay in the presence of degeneracie
\inbook Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2025
\vol 239
\pages 25--31
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1335}
\crossref{https://doi.org/10.36535/2782-4438-2025-239-25-31}
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