| Abstract: |
| In this talk, we will consider the study of the 2-D Schr\{o}dinger-Poisson equation with critical exponential growth. By variational methods, we first prove the existence of ground state solutions for this Schr\{o}dinger-Poisson system with the periodic potential. Then we obtain that there exists a positive ground state solution of the Schr\{o}dinger-Poisson system concentrating at a global minimum of potential function in the semi-classical limit under some suitable conditions. Meanwhile, the exponential decay of this ground state solution is detected. Finally, we establish the multiplicity of positive solutions by using the Ljusternik-Schnirelmann theory. |
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