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

[1] A. A. Agrachev, R. V. Gamkrelidze, “Printsip optimalnosti vtorogo poryadka dlya zadachi bystrodeistviya”, Matem. sb., 100(142) (1976), 610–643 | Zbl

[2] R. V. Gamkrelidze, G. L. Kharatishvili, “Ekstremalnye zadachi v lineinykh topologicheskikh prostranstvakh”, Izv. AN SSSR, seriya matem., 33 (1969), 781–839 | MR | Zbl

[3] R. V. Gamkrelidze, Osnovy optimalnogo upravleniya, izd-vo Tbil. un-ta, Tbilisi, 1975 | MR