Question: 2. Consider the minimisation problem find u V such that J(u) J(v) v V, where J: H(0, 1) R is the functional defined by

2. Consider the minimisation problem find u V such that J(u) J(v) v V, where J: H(0, 1) R is the functional defined by J(n) := f (7) dx - f" fndx, with f L(0, 1) and V:= {v H(0, 1) [v(0) = v(1) = 0 and '(0) = v' (1) = 0} . (3) (iv) Suppose we take V := H(0, 1) how many solutions would one expect to (3)? Give a brief justification of your answer.

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