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.
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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