I am having a hard time getting my head around Functionals and Calculus of Variations,
My question is: Given a functional and using the Euler-Lagrange equation to find an extremal, how do we show that the extremal provides a min/max (if it does)
The question I am working on is
I found the extremal to be: which I am told is a minimum to the functional problem.
However I am unsure on what is sufficient to show this, in the notes I have it is shown that:
where f is continuously differentiable on the interval 0,1 with
Thanks in advance!