Multiple positive solutions for a logarithmic Schrödinger–Poisson
system with singular nonelinearity
Keyword(s):
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.
2008 ◽
Vol 39
(2)
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pp. 111-120
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2017 ◽
Vol 24
(3)
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pp. 313-323
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