3

Is there any standard approach to solve the following kind of variational problem?

Maximize $F=\int_0 ^1 L(x,y,y')dx $ subject to the constraint $|\int_0 ^1 M(x,y,y')dx| \lt k$ where $y$ is the function of $x$ to be solved for.

I can think immediately of maximizing $\int_0 ^1 Ldx + \lambda(\int_0^1 Mdx-k)^2 $ but don't know whether that will yield the right solution. I can't seem to find this kind of problem solved in the usual references, e.g. Bruce Van Brunt's Calculus of Variations.

Ganesh
  • 1,721
  • How about first looking for an unconstrained maximum of $F$ and seeing if it satisfies the constraint? Then try the constrained problems $\max F ,| \int M = k$ and $\max F ,| \int M = -k$ separately. – kiwi Apr 07 '12 at 18:47
  • Also you can use – mike Jan 12 '17 at 20:26

0 Answers0