On solvability of one class of third order differential equations
Анотація
УДК 517.9
Про розв’язнiсть одного класу диференцiальних рiвнянь третього порядку
Розглянуто одновимірну мішану задачу для одного класу диференціальних рівнянь третього порядку з частинними похідними з нелінійною правою частиною. Введено поняття узагальненого розв'язку для цієї задачі. За допомогою методу Фур'є задачу існування та єдиності узагальненого розв'язку зведено до задачі розв'язності зліченної системи нелінійних інтегро-диференціальних рівнянь. З використанням нерівності Беллмана доведено єдиність узагальненого розв'язку. При деяких умовах на початкові функції та праву частину рівняння на основі методу послідовних ітерацій доведено теорему про існування узагальненого розв'язку.
Посилання
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