Construction of solutions to a nonlinear critical elliptic system via local Pohozaev identities

Qidong Guo, Qingfang Wang, Wenju Wu

In this paper, we investigate the following elliptic system with Sobolev critical growth $-\Delta u+P(|y^{\prime }|,y^{\prime \prime })u=u^{2^{\ast }-1}+\frac{\beta }{2}{u}^{\frac{2^{\ast }}{2}-1}{v}^{\frac{2^{\ast }}{2}},y\in R^N$, $-Δ…