Geodesic
A~second-order necessary condition for optimality in the general nonlinear case
Sbornik. Mathematics, Tome 31 (1977) no. 4, pp. 493-506

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In this paper a second-order optimality condition is obtained for the general nonlinear problem with arbitrary boundary conditions and an integral-type minimized functional. Moreover, a second-order sufficient condition for controllability is derived. Bibliography: 3 titles. 
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     author = {A. A. Agrachev},
     title = {A~second-order necessary condition for optimality in the general nonlinear case},
     journal = {Sbornik. Mathematics},
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     volume = {31},
     number = {4},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_31_4_a4/}
}
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A. A. Agrachev. A~second-order necessary condition for optimality in the general nonlinear case. Sbornik. Mathematics, Tome 31 (1977) no. 4, pp. 493-506. http://geodesic.mathdoc.fr/item/SM_1977_31_4_a4/