I've used Euler-Lagrange and can't seem to get the right answer, please help if you can.

Determine the extremal for the functional

with

Using Euler-Lagrange I get,

but that isn't consistent with the given b.c.s

Please help!

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- Nov 6th 2011, 04:39 AMfeatherboxFind the extremal of this functional with given b.c.s
I've used Euler-Lagrange and can't seem to get the right answer, please help if you can.

Determine the extremal for the functional

with

Using Euler-Lagrange I get,

but that isn't consistent with the given b.c.s

Please help! - Nov 7th 2011, 04:11 AMAckbeetRe: Find the extremal of this functional with given b.c.s
Actually, this should be

but you seem to have computed the correct expression here:

Quote:

So the problem reduces down to finding the extremal of

subject to the boundary conditions. Since there is now no term, the Euler-Lagrange equation simplifies down to setting

which implies

or as before. And, as you've noted, this function does not satisfy the boundary conditions.

Question: what is the domain of functions over which you're searching for a solution? Continuous? Differentiable? (I would assume probably differentiable, since you have a in the integrand; however, you might be interpreting that derivative in a weak sense, or in some other similarly exotic fashion.)

If you require a differentiable function as your solution, then I would say your problem has no solution.