We consider the following nonlinear biharmonic equations:
$$ \Delta^{2} u-\Delta u+ V_{\lambda }(x)u=f(x,u),\quad \text{in } \mathbb{R}^{N}, $$
where
$V_{\lambda }(x)$
is allowed to be sign-changing and f is an indefinite function. Under some suitable assumptions, the existence of nontrivial solutions and the high energy solutions are obtained by using variational methods. Moreover, the phenomenon of concentration of solutions is explored. The results extend the main conclusions in recent literature.
