Schrödinger-Poisson systems in $4$-dimensional closed manifolds
Pierre-Damien Thizy
Discrete & Continuous Dynamical Systems - A 2016, 36(4): 2257-2284 doi: 10.3934/dcds.2016.36.2257
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: Nonlinear elliptic PDE's Schrödinger-Poisson solitary waves. non-resonant states analysis on manifolds critical systems
Klein-Gordon-Maxwell equations in high dimensions
Pierre-Damien Thizy
Communications on Pure & Applied Analysis 2015, 14(3): 1097-1125 doi: 10.3934/cpaa.2015.14.1097
We prove the existence of a mountain-pass solution and the a priori bound property for the electrostatic Klein-Gordon-Maxwell equations in high dimensions.
keywords: non-resonant states Klein-Gordon-Maxwell analysis on manifolds critical systems solitary waves. Nonlinear elliptic PDE's

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