Sistemy Differentsial'nykh Uravneniy S Obobshchennymi Koeffitsientami

S tochki zreniya klassicheskoy teorii differentsial'nykh uravneniy sistemy differentsial'nykh uravneniy, soderzhashchie proizvedenie obobshchennykh funktsiy yavlyayutsya nekorrektnymi, v svyazi s etim voznikaet neobkhodimost' korrektnogo opredeleniya ukazannogo tipa sistem, poskol'ku poluchaemoe reshenie sushchestvenno zavisit ot ispol'zuemogo sposoba opredeleniya proizvedeniya. V nastoyashchee vremya odno iz napravleniy issledovaniya differentsial'nykh uravneniy s obobshchennymi koeffitsientami predpolagaet ikh izuchenie v ramkakh teorii algebr novykh obobshchennykh funktsiy ili mnemofunktsiy. Dannaya kniga posvyashchena issledovaniyu zadachi Koshi dlya sistem differentsial'nykh uravneniy s obobshchennymi koeffitsientami i sistem differentsial'nykh vklyucheniy s obobshchennoy pravoy chast'yu v pryamom proizvedenii algebr mnemofunktsiy. V knige provoditsya klassifikatsiya assotsiirovannykh resheniy ukazannykh sistem v pryamom proizvedenii algebr mnemofunktsiy v sluchayakh kogda pravaya chast' soderzhit proizvedenie lipshitsevykh funktsiy i obobshchennykh proizvodnykh funktsiy ogranichennoy variatsii, razryvnykh funktsiy i obobshchennykh proizvodnykh nepreryvnykh funktsiy ogranichennoy variatsii, razryvnykh funktsiy i obobshchennykh proizvodnykh kusochno-postoyannykh funktsiy.