On the exterior Neumann problem involving the critical Sobolev exponent (Q1882610)

The authors deal with the existence of solutions of the exterior Neumann problem \[ -\Delta u+au=Q\cdot|u|^{2^*-2}\cdot u,\text{ in }\Omega^c\quad\frac{\partial u}{\partial n}=0,\text{ on }\partial \Omega,\tag{1} \] where \(\Omega^c=\mathbb R^N \setminus\Omega\) with \(\Omega\) being smooth bounded domain in \(\mathbb R^N\), \(N\geq 3\), the value \(2^*\) is the critical Sobolev exponent, \(Q\) and \(a\) are given real functions satisfying natural assumptions.