List of issues > Series «Mathematics». 2010. Vol. 2
On solvability of essentially degenerate nonlinear algebraic differential system
We consider nonlinear system of ordinary differential equations, which is not solved with respect to the derivative of the desired vector function and identically
degenerate in the domain of definition. Under the assumption that the initial data generate a solution of the maltiplicity grater than one for the corresponding finite-
dimensional system, the process of transformation of the given system into the system in the normal form is suggested, the theorem of existence of a solution to a Cauchy problem is proved.
1. Бояринцев, Ю.Е. Методы решения вырожденных систем обыкновенных диф-ференциальных уравнений / Ю.Е. Бояринцев. – Новосибирск : Наука, 1988. –158 с.
2. Кудрявцев, Л.Д. Курс математического анализа, т. II. / Л.Д. Кудрявцев. – М.:Высшая школа, 1981. – 584 с.
3. Чистяков, В.Ф. Алгебро-дифференциальные операторы с конечномерным яд-ром / В.Ф. Чистяков. – Новосибирск: Hаука, 1996. – 279 c.
4. Шилов, Г.Е. Математический анализ (функции нескольких вещественныхпеременных), части 1-2 / Г.Е. Шилов. – М.: Наука, 1972. – 624 с.
5. Brenan, K.E. Numerical Solution of Initial - Value Problems in Differential -Algebraic Equations (Classics in applied mathematics 14) / K.E. Brenan, S.L.Campbell, L.R. Petzold. Philadelphia: SIAM, 1996. – 256 p.