This article is cited in 7 papers

The Euler–Jacobi equation in variational calculus

A. V. Dmitruk

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 519.3

Received: 31.10.1975

 English version: Mathematical Notes, 1976, 20:6, 1032–1038

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