The Euler-Jacobi equation in variational calculus

The use of the method of the Euler-Jacobi equation is considered in the study of a quadratic functional defined on a cone. Such functionals occur in the variation of optimal-control problems. Several concepts are introduced with the aid of which the Euler-Jacobi equation is extended and the application of this method is justified also in the case that the equation is not a linear differential equation.Translated from Matematicheskie Zametki, Vol. 20, No. 6, pp. 847–858, December, 1976.