On the uniqueness of the solution of nonlinear differential-algebraic systems
We consider the Cauchy problem for a system of nonlinear ordinary differential equations unsolved for the derivative of the unknown vector function and identically degenerate in the domain. We prove a theorem on the coincidence of two smooth solutions of the considered problem. We show that, under some additional assumptions, the above-mentioned problem cannot have classical solutions with less smoothness. We obtain conditions under which the problem has a fixed finite number of solutions.
KeywordsCauchy Problem Implicit Function Theorem Continuous Partial Derivative Permutation Matrice Independent Column
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