@article{Chabrowski_Szulkin_Willem_2009, title={Schrödinger equation with multiparticle potential and critical nonlinearity}, volume={34}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2009.038}, abstractNote={We study the existence and non-existence of ground states for the Schrödinger equations $-\Delta u -\lambda\sum_{i< j}u/|x_i-x_j|^2 = |u|^{2^*-2}u$, $x=(x_1,\ldots,x_m)\in {\mathbb R}^{mN}$, and $-\Delta u -\lambda u/|y|^2 = |u|^{2^*-2}u,\quad x=(y,z)\in {\mathbb R}^N$. In both cases we assume $\lambda e 0$ and $\lambda< \overline\lambda$, where $\overline\lambda$ is the Hardy constant corresponding to the problem.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Chabrowski, Jan and Szulkin, Andrzej and Willem, Michael}, year={2009}, month={Dec.}, pages={201–211} }