The Lemmas of Lagrange and du Bois-Reymond

Abstract

In most of the examples in Chapter 3, we examined a real valued function F defined on a domain of functions $\mathcal{D}$ and obtained for it an integral condition in the form I(y, v) = 0, ∀ v in an auxiliary domain $\mathcal{D}$₀ which is sufficient to guarantee that each y ∈ $\mathcal{D}$ which satisfies it must minimize F on $\mathcal{D}$.