Multiple positive solutions for a logarithmic Schrödinger–Poisson system with singular nonelinearity

In this article, we devote ourselves to investigate the followinglogarithmic Schrödinger–Poisson systems with singular nonlinearity { − Δ u + ϕ u = | u | p − 2 u log ⁡ | u | + λ u γ , i n   Ω , − Δ ϕ = u 2 , i n   Ω , u = ϕ = 0 , o n   ∂ Ω , where Ω is a smooth bounded domain with boundary 0 < γ < 1 , p ∈ ( 4 , 6 ) and λ > 0 is a real parameter. By using the critical point theory for nonsmooth functionaland variational method, the existence and multiplicity of positivesolutions are established.