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

Pierre-Damien Thizy

doi:10.3934/dcds.2016.36.2257

Article Contents

2016, Volume 36, Issue 4: 2257-2284. Doi: 10.3934/dcds.2016.36.2257

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

Pierre-Damien Thizy^1,

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

Received: December 31, 2014

Revised: March 31, 2015

Published: May 2017

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 58J05; Secondary: 35J47, 35Q61, 35R01, 58J37, 81Q35.

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