Bolza Problem

Given the functional

U=int_(t_0)^(t_1)f(y_1,...,y_n;y_1^',...,y_n^')dt+G(y_(10),...,y_(nr);y_(11),...,y_(n1)),

(1)

find in a class of arcs satisfying p differential and q finite equations

(2)

as well as the r equations on the endpoints

chi_gamma(y_(10),...,y_(nr);y_(11),...,y_(n1))=0 for gamma=1,...,r,

(3)

which renders U a minimum.

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

Goldstine, H. H. A History of the Calculus of Variations from the 17th through the 19th Century. New York: Springer-Verlag, p. 374, 1980.