On a logarithmic Hartree equation

Abstract

We study the existence of radially symmetric solutions for a nonlinear planar Schrödinger-Poisson system in presence of a superlinear reaction term which doesn’t satisfy the Ambrosetti-Rabinowitz condition. The system is re-written as a nonlinear Hartree equation with a logarithmic convolution term, and the existence of a positive and a negative solution is established via critical point theory.

Keywords

• planar schrödinger-poisson system
• logarithmic hartree equation
• hardy-littlewood-sobolev inequality
• superlinear source
• 35j50
• 35q40