  We examine the equation \[\Delta^2 u = \lambda f(u) \qquad \Omega, \] with
either Navier or Dirichlet boundary conditions. We show some uniqueness results
under certain constraints on the parameter $ \lambda$. We obtain similar
results for the sytem
  {equation*} \{{array}{rrl} -\Delta u &=& \lambda f(v) \qquad \Omega, -\Delta
v &=& \gamma g(u) \qquad \Omega, u&=& v = 0 \qquad \partial Omega. {array}.
{equation*}
