Consider the problem of minimizing

∫(y"(x))2(1 − (y"(x))2)dx, (lower limit=0,upper limit=1)

subject to y(0) = y(1) = 0. Is the curve y(x) 5 0 a weak minimum (over C1 curves)? Is it a strong

minimum (over a.e. C1 curves)? Is there another curve that is a strong minimum?

how to solve that problem? how to check the existence for the strong and week extrema?

thanks in advance.regards.