  Using direct variational method we consider the existence of non-spurious
solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left(
t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where
$f:\left[ 0,1\right] \times \mathbb{R} \rightarrow \mathbb{R}$ is a jointly
continuous function convex in $x$ which does not need to satisfy any further
growth conditions.
