Multiple solutions for planar Schrodinger-Poisson system with logarithmic nonlinearity

Wei Long, Changchang Yan, Jianghua Ye

This paper is concerned with the following planar Schrodinger-Poisson system: $\{\begin{array}{ll}-\Delta u+V(x)u+\lambda \varphi u=u\ln u^2,& \text{in }{R}^2,\\ \Delta \varphi =u^2,& \text{in }{R}^2.\end{array}$ w…