Geodesic
Necessary conditions for a minimum in variational problems with delay in the presence of degeneracie
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Tome 239 (2025), pp. 25-31

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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 
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     author = {M. J. Mardanov and T. K. Melikov},
     title = {Necessary conditions for a minimum in variational problems with delay in the presence of degeneracie},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {25--31},
     publisher = {mathdoc},
     volume = {239},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2025_239_a2/}
}
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M. J. Mardanov; T. K. Melikov. Necessary conditions for a minimum in variational problems with delay in the presence of degeneracie. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 2, Tome 239 (2025), pp. 25-31. http://geodesic.mathdoc.fr/item/INTO_2025_239_a2/