Valeriy Obukhovskiy

Topologicheskie Metody V Kraevykh Zadachakh Dlya Differentsial'nykh Vklyucheniy: Vvedenie V Elementy Nelineynogo Analiza Valeriy Obukhovskiy Russian edition

Teoriya differentsial'nykh vklyucheniy yavlyaetsya vazhnoy chast'yu sovremennoy matematiki, blagodarya, v chastnosti, svoim prilozheniyam k sistemam upravleniya. Primenenie geometricheskikh i topologicheskikh metodov analiza k issledovaniyu razlichnykh voprosov teorii differentsial'nykh vklyucheniy imeet davnyuyu istoriyu. S pomoshch'yu ukazannykh metodov okazalos' vozmozhnym effektivno reshat' vazhnye problemy teorii differentsial'nykh vklyucheniy. Nastoyashchaya kniga posvyashchena, vo-pervykh, podrobnomu i dostupnomu dlya ne spetsialista izlozheniyu primenyaemykh topologicheskikh sredstv, vklyuchaya teoriyu topologicheskoy stepeni dlya dostatochno shirokogo klassa mnogoznachnykh otobrazheniy. V osnovnoy zhe svoey chasti, kniga soderzhit prilozheniya razvitykh metodov k obshchim kraevym zadacham dlya funktsional'no-differentsial'nykh vklyucheniy. Dannye zadachi vklyuchayut v sebya, v chastnosti, klassicheskie zadachu Koshi i periodicheskuyu zadachu i ikh nekotorye obobshcheniya. Rassmotreny prilozheniya k sushchestvovaniyu optimal'nogo resheniya dlya upravlyaemoy sistemy s razryvnymi kharakteristikami. Kniga rasschitana na shirokiy krug chitateley, interesuyushchikhsya voprosami sovremennogo nelineynogo i mnogoznachnogo analiza i ikh prilozheniyami k zadacham upravleniya slozhnymi sistemami.