Geodesic
P-order necessary and sufficient conditions for optimality in singular calculus of variations
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 30 (2010) no. 2, pp. 269-279.

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This paper is devoted to singular calculus of variations problems with constraint functional not regular at the solution point in the sense that the first derivative is not surjective. In the first part of the paper we pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we formulate and prove necessary and sufficient conditions for optimality in singular case and illustrate our results by classical example of calculus of variations problem.
Keywords: singular variational problem, necessary condition of optimality, p-regularity, p-factor operator 
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Prusińska, Agnieszka; Tret'yakov, Alexey. P-order necessary and sufficient conditions for optimality in singular calculus of variations. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 30 (2010) no. 2, pp. 269-279. http://geodesic.mathdoc.fr/item/DMDICO_2010_30_2_a6/

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