Multiple solutions for planar Schrodinger-Poisson system with logarithmic nonlinearity

This paper is concerned with the following planar Schrodinger-Poisson system: $\begin{cases} -Δu +V(x)u+λϕu=u\ln u^2, & \text{in }{R}^2,\\ Δϕ=u^2, & \text{in }{R}^2. \end{cases}$ where $λ\in{R}$ is a parameter and $V\in C^1({R}^2,R}^{+})$ is a coercive potential. Due to the presence of the logarithm