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  Proceedings of the International Conference on the Calculus of Variations and Related Topics,
  Haifa, March 1998

  For singular extremals in the above class of problems conditions of a Pontryagin minimum include
  a new pointwise condition, i.e. a condition of Legendre type. It involves not only the second,
  but also the third variation of Lagrange function, and requires to solve a nontrivial auxiliary
  optimal control problem. Some cases of its exact solution are presented.

  Key words:
    singular extremal, weak and Pontryagin minimum, quadratic order of estimation,
    necessary and sufficient conditions, second and third variations of Lagrange function.

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