Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term

2017/02/13 by Shen, Liejun, Yao, Xiaohua
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.03792

Abstract

The present study is concerned with the following Schrödinger-Poisson system involving critical nonlocal term \ -Δu+u-K(x)ϕ|u|³u=λf(x)|u|^q-2u, · amp; x∈ℝ³, -Δϕ=K(x)|u|⁵, · amp; x∈ℝ³, . where 10 is a parameter. Under suitable assumptions on K(x) and f(x), there exists λ₀=λ₀(q,S,f,K)>0 such that for any λ∈(0,λ₀), the above Schrödinger-Poisson system possesses at least two positive solutions by standard variational method, where a positive least energy solution will also be obtained.

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