DCDS
Schrödinger-Poisson systems in $4$-dimensional closed manifolds
Pierre-Damien Thizy
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
CPAA
Klein-Gordon-Maxwell equations in high dimensions
Pierre-Damien Thizy
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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