Normality and abnormality in the calculus of variations

Abstract

Within the past few years a number of papers concerning the problem of Bolza in the calculus of variations have been published which make it possible to carry through the theory of this problem with much simplified assumptions concerning what is called the normality of the minimizing arc. I refer especially to papers by Graves Hestenes [11, 14, 16], Reid [15], and Morse [13]. These papers and others are also important because they bring the theory of problems of the calculus of variations with variable end points to a stage comparable with that already attained for the more special case in which the end points are fixed.