On the inverse problem for even-order ordinary differential equations in the higher-order calculus of variations

Abstract

A paper of Anderson and Thompson demonstrates that the inverse problem in the calculus of variations for systems of fourth-order ordinary differential equations gives rise to a system of PDEs in Frobenius form for the multiplier functions, and therefore has a structure much simpler than that of the corresponding problem for second-order equations. We show that a similar simplification holds for systems of equations of order 2 k ( k>2).