  We study the existence/nonexistence of positive solution to the problem of
the type: \begin{equation}\tag{$P_{\lambda}$} \begin{cases} \Delta^2u-\mu
a(x)u=f(u)+\lambda b(x)\quad\textrm{in $\Omega$,}\\ u>0 \quad\textrm{in
$\Omega$,}\\ u=0=\Delta u \quad\textrm{on $\partial\Omega$,} \end{cases}
\end{equation} where $\Omega$ is a smooth bounded domain in $\mathbb R^N$,
$N\geq 5$, $a, b, f$ are nonnegaive functions satisfying certain hypothesis
which we will specify later. $\mu,\lambda$ are positive constants. Under some
suitable conditions on functions $a, b, f$ and the constant $\mu$, we show that
there exists $\lambda^*>0$ such that when $0<\lambda<\lambda^*$,
($P_{\lambda}$) admits a solution in $W^{2,2}(\Omega)\cap W^{1,2}_0(\Omega)$
and for $\lambda>\lambda^*$, it does not have any solution in
$W^{2,2}(\Omega)\cap W^{1,2}_0(\Omega)$. Moreover as
$\lambda\uparrow\lambda^*$, minimal positive solution of ($P_{\lambda}$)
converges in $W^{2,2}(\Omega)\cap W^{1,2}_0(\Omega)$ to a solution of
($P_{\lambda^*}$). We also prove that there exists $\tilde{\lambda}^*<\infty$
such that $\lambda^*\leq\tilde{\lambda}^*$ and for $\lambda>\tilde{\lambda}^*$,
the above problem ($P_{\lambda}$) does not have any solution even in the
distributional sense/very weak sense and there is complete {\it blow-up}. Under
an additional integrability condition on $b$, we establish the uniqueness of
positive solution of ($P_{\lambda^*}$) in $W^{2,2}(\Omega)\cap
W^{1,2}_0(\Omega)$.
