Topic
Legendre–Clebsch condition
About: Legendre–Clebsch condition is a research topic. Over the lifetime, 175 publications have been published within this topic receiving 6117 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the Euler-Lagrange type necessary conditions which must be satisfied for the given functional to be extremum were developed for systems containing fractional derivatives, where the fractional derivative is described in the Riemann-Liouville sense.
866 citations
TL;DR: In this article, it was shown that the functional equation approach yields, in simple and intuitive fashion, formal derivations of such classical necessary conditions of the Calculus of Variations as the Euler-Lagrange equations, the Weierstrass and Legendre conditions, natural boundary conditions, a transversality condition and the Erdmann corner conditions.
312 citations
TL;DR: In this paper, a linear differential system e on which the inverse problem can be made to depend has been derived, based on the Riquier theory of systems of partial differential equations.
Abstract: Our essential results and methods have already been published in two preliminary notes('). Basically, our procedure consists in an application of the Riquier theory of systems of partial differential equations to a certain linear differential system e on which the inverse problem can be made to depend. This differential system has already appeared-derived in a different way-in the interesting work, of little more than a decade ago, by D. R. Davis on the inverse problem(2); but, as he stated, its general solution-even existence-theoreticallypresented difficulties which he could not overcome.
308 citations
TL;DR: In this paper, the authors developed some basics of discrete fractional calculus such as Leibniz rule and summation by parts formula and derived Euler-Lagrange equation.
287 citations
01 Jan 1993
TL;DR: The Legendre condition as discussed by the authors is a necessary condition for the solution of the Euler equation (16.1), and the Transversality condition is sufficient for the transversality.
Abstract: The Euler equation. A necessary condition for the solution of (16.1). An alternative form of the Euler equation. The Legendre condition. A necessary condition for the solution of (16.1). Sufficient conditions for the solution of (16.1). Transversality condition. Adding condition (16.5) gives sufficient conditions.
274 citations