Solution
= Solution
The continuous superlinear function $\Phi$ tends to positive infinity at both ends, so it has a finite global minimum $M$. Hence $I(u)\geq M(b-a)$ for every admissible function. An affine function with the prescribed endpoints is Lipschitz and has finite energy by continuity of the integrand on its compact range. Thus
$$
\boxed{-\infty<M(b-a)\leq l<\infty,}
$$
where the strict left inequality simply records finiteness of $M$.