Existence of multi-bump solutions to biharmonic operator with critical   exponential growth in $\mathbb{R}^4$
  Using variational methods, we establish existence of multi-bump solutions for the following class of problems $$   \left\{   \begin{array}{l}   \Delta^2 u +(\lambda V(x)+1)u = f(u), \quad \mbox{in} \quad \mathbb{R}^{4},   u \in H^{2}(\mathbb{R}^{4}),   \end{array}   \right.   $$ where $\Delta^2$ is the biharmonic operator, $f$ is a continuous function with critical exponential growth and $V : \mathbb{R}^4 \rightarrow \mathbb{R}$ is a continuous function verifying some conditions. 
Al\^annio B. N\'obrega and Denilson S. Pereira
math.AP