Existence of positive solutions to Schrödinger-Poisson type systems with critical exponent.

The existence of positive solutions to Schrödinger-Poisson type systems in ℝ3 with critically growing nonlocal term is proved by using variational method which does not require usual compactness conditions. A key ingredient of the proof is a new Brézis-Lieb type convergence result. [ABSTRACT FROM AUTHOR]