Concentration of solutions for a fourth order elliptic equation in ${\mathbb{R}}^N$

Abstract

In this paper, we study the following fourth order elliptic problem $${\Delta }^{2}u=(1+\epsilon K(x))u^{2^{\ast }-1},x\in {\mathbb{R}}^N$$ where $2^{\ast }=\frac{2N}{N-4}$,$N\ge 5$, $\epsilon >0$. We prove that the existence of two peaks solutions for the above problem, if $K(x)$ has two critical points satisfying certain conditions, provided $\epsilon$ is small enough.

19 pages