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Article ID: CBB728454472

Karamata Functions and Differential Equations: Achievements from the 20th Century (2018)

Nikolić, Aleksandar M. (Author)

Historia Mathematica
Volume: 45
Issue: 3
Pages: 277-299

URI: https://www.sciencedirect.com/science/article/pii/S0315086017301155

DOI: 10.1016/j.hm.2017.12.001

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This paper presents the major achievements of the 20th century regarding Karamata functions and the theory of differential equations, made mostly by V. Marić, M. Tomić, E. Omey, J.L. Geluk. The connection between these notions was first noticed by V.G. Avakumović (1910–1990). Slowly and regularly varying functions were introduced by J. Karamata (1902–1967). A group of mathematicians from the Karamata School of classical mathematical analysis were pioneers in research on these functions and their role in the theory of differential equations. Special attentions is given to the study of the Thomas–Fermi, Emden–Fowler and Friedmann equations, as well as the classical second order linear differential equations. U radu su prikazani glavni rezultati istraživanja veze Karamatinih funkcija i teorije diferencijalnih jednačina koji su nastali u 20. veku i čiji su najznačajniji autori bili: V. Marić, M. Tomić, E. Omey, J.L. Geluk. Vezu ove dve oblasti matematičke analize prvi je uočio V.G. Avakumović (1910–1990). Pravilnopromenljive funkcije definisao je i njihova bitna svojstva dao J. Karamata (1902–1967). Grupa matematičara iz Karamatine škole klasične matematičke analize prvi su proučavali te funkcije i njihovu ulogu u teoriji diferencijalnih jednačina. Posebno su značajne Tomas–Fermijeva, Emden–Faulerova i Fridmanova diferencijalne jednačine, kao i klasična linearna diferencijalna jednačina drugog reda.

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