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

• Published in: Electronic journal of qualitative theory of differential equations Vol. 2021; no. 90; pp. 1 - 15
• Main Authors: Peng, Linyan, Suo, Hongmin, Wu, Deke, Feng, Hongxi, Lei, Chunyu
• Format: Journal Article
• Language: English
• Published: University of Szeged 01.12.2021
• Subjects: logarithmic schrödinger–poisson system; multiplicity; positive solutions; singularity
• ISSN: 1417-3875; 1417-3875
• DOI: 10.14232/ejqtde.2021.1.90

In this article, we devote ourselves to investigate the following logarithmic 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 functional and variational method, the existence and multiplicity of positive solutions are established.