Sufficient conditions for weak minimum of a functional depending on n functions and their derivatives

Abstract

The sufficient condition for positive definiteness of a quadratic form involving unsymmetric matrix operators is given in terms of a global criterion. This determines the sufficient condition for the weak minimum of a functional depending on n-functions and their derivatives. The criterion is formulated in terms of the absence of conjugate points in the interval of the variational integral and is a generalization of a similar criterion due to Newcomb in problems of hydromagnetic stability in plasma physics.