  In this paper, we study the following biharmonic equations:% $$
\left\{\aligned&\Delta^2u-a_0\Delta u+(\lambda b(x)+b_0)u=f(u)&\text{ in
}\bbr^N,\\% &u\in\h,\endaligned\right.\eqno{(\mathcal{P}_{\lambda})}% $$ where
$N\geq3$, $a_0,b_0\in\bbr$ are two constants, $\lambda>0$ is a parameter,
$b(x)\geq0$ is a potential well and $f(t)\in C(\bbr)$ is subcritical and
superlinear or asymptotically linear at infinity. By the Gagliardo-Nirenberg
inequality, we make some observations on the operator
$\Delta^2-a_0\Delta+\lambda b(x)+b_0$ in $\h$. Based on these observations, we
give a new variational setting to $(\mathcal{P}_{\lambda})$ for $a_0<0$. With
this new variational setting in hands, we establish some new existence results
of the nontrivial solutions to $(\mathcal{P}_{\lambda})$ for all $a_0,
b_0\in\bbr$ with $\lambda$ sufficiently large by the variational method. The
concentration behavior of the nontrivial solutions as $\lambda\to+\infty$ is
also obtained. It is worth to point out that it seems to be the first time that
the nontrivial solution of $(\mathcal{P}_{\lambda})$ is obtained in the case of
$a_0<0$.
