- #1
daudaudaudau
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Homework Statement
Consider the functional defined by
[tex]
J(y)=\int_{-1}^1 x^4(y'(x))^2 dx
[/tex]
Without resorting to the Euler-Lagrange equation, prove that J cannot have a local minimum in the set
[tex]
S=\{y\in C^2[-1,1]:\ y(-1)=-1,\ y(1)=1\}.
[/tex]
The Attempt at a Solution
I have thought about this one, but I have no clue how to do it without the Euler-Lagrange equation. Using the EL equation, I can find a solution which satisfies the boundary conditions, but is not continuous at [itex]x=0[/itex]: [itex]y=1/x^3[/itex].