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.
Bernini, F., Mugnai, D. (2020). On a logarithmic Hartree equation. ADVANCES IN NONLINEAR ANALYSIS, 9(1), 850-865 [10.1515/anona-2020-0028].
On a logarithmic Hartree equation
BERNINI, FEDERICO;
2020
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.
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