TY - JOUR AU - Chabrowski, Jan AU - Szulkin, Andrzej AU - Willem, Michael PY - 2009/12/01 Y2 - 2024/03/29 TI - Schrödinger equation with multiparticle potential and critical nonlinearity JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 34 IS - 2 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2009.038 SP - 201 - 211 AB - 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. ER -