# American Institute of Mathematical Sciences

April  2016, 36(4): 2257-2284. doi: 10.3934/dcds.2016.36.2257

## Schrödinger-Poisson systems in $4$-dimensional closed manifolds

 1 Université de Cergy-Pontoise, CNRS, Département de Mathématiques, F-95000 Cergy-Pontoise

Received  January 2015 Revised  April 2015 Published  September 2015

We investigate existence, nonexistence and uniqueness of positive solutions of critical Schrödinger-Poisson systems in closed $4$-manifolds. In the process we provide a sharp criterion for the non-existence of resonant states.
Citation: Pierre-Damien Thizy. Schrödinger-Poisson systems in $4$-dimensional closed manifolds. Discrete & Continuous Dynamical Systems, 2016, 36 (4) : 2257-2284. doi: 10.3934/dcds.2016.36.2257
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