Standing Waves for nonlinear Schrodinger Equations involving critical   growth
  We consider the following singularly perturbed nonlinear elliptic problem: $$-\e^2\Delta u+V(x)u=f(u),\ u\in H^1(\mathbb{R^N}),$$ where $N\ge 3$ and the nonlinearity $f$ is of critical growth. In this paper, we construct a solution $u_\e$ of the above problem which concentrates at an isolated component of positive local minimum points of $V$ as $\e\to 0$ under certain conditions on $f$. Our result completes the study made in some very recent works in the sense that, in those papers only the subcritical growth was considered 
Jianjun Zhang and Zhijie Chen and Wenming Zou
math.AP