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It is shown that the planar Schrodinger-Poisson system with a general nonlinear interaction function has a nontrivial solution of mountain-pass type and a ground state solution of Nehari-Pohozaev type. The conditions on the nonlinear functions are much weaker and flexible than previous ones, and new variational and analytic techniques are used in the proof.

Ground state solutions of Nehari-Pohozaev type for the planar Schrödinger-Poisson system with general nonlinearity