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.