Differential Equations

, Volume 46, Issue 2, pp 195–207 | Cite as

On the uniqueness of the solution of nonlinear differential-algebraic systems

  • A. A. Shcheglova
Ordinary Differential Equations


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.


Cauchy Problem Implicit Function Theorem Continuous Partial Derivative Permutation Matrice Independent Column 
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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. A. Shcheglova
    • 1
  1. 1.Institute for System Dynamics and Control Theory Siberian BranchRussian Academy of SciencesIrkutskRussia

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