Title: "A fixed-endpoint, autonomous problem in the one-dimensional problem in the Calculus of Variations."

Abstract: I present in detail an elementary fixed-endpoint, autonomous problem in the one-dimensional Calculus of Variations for which there is a continuum of piecewise-linear solutions of the Euler-Lagrange equation, each providing a weak local minimum, and each with a different integral value. Along most of these solutions the Hamiltonian is not constant! This puts the spotlight on the difference between weak and strong local minimizers, and reveals some unfortunate errors in current textbooks.