| Abstract: | For problems in the calculus of variations withisoperimetric side constraints, we provide in this paper a set ofpoints whose emptiness, independently of nonsingularity assumptions,is equivalent to the nonnegativity of the second variation alongadmissible variations. The main objective of introducing acharacterization of this condition should be, of course, to obtain asimpler way of verifying it. There are two other sets of pointsavailable in the literature, introduced by Loewen and Zheng (1994)and Zeidan (1996), for which this necessary condition implies theiremptiness. However, we show that verifying membership of these setsmay be more difficult than checking directly if that conditionholds. Contrary to this behavior, we prove that the desiredobjective of characterizing that condition is achieved by means ofthe set introduced in this paper. |
