On solvability of essentially degenerate nonlinear algebraic differential system (Q446323)

A nonlinear system of ordinary differential equations, which is not solved with respect to the derivative of the desired vector function and identically degenerates in the domain of definition is considered. Under the assumption that the initial data generate a solution of multiplicity greater than one for the corresponding finite-dimensional system, the process of transformation of the given system into a system of normal form is suggested. A theorem on the existence of a solution to the Cauchy problem is proved.