Abstract
A uniqueness result for a Schrödinger–Poisson system with strong singularity
Highlights
A necessary and sufficient condition on the existence and uniqueness of positive weak solution of the system is obtained
In this paper, we consider the existence and uniqueness of positive solution for the following Schrödinger–Poisson system −∆u + φu (SP) u > 0, x ∈ Ω,u = φ = 0, x ∈ ∂Ω, S
When g(x, u) = 0, f (x) = μ is a positive parameter and 0 < γ < 1, Zhang [28] obtained a sufficient condition on the existence, uniqueness and multiplicity of positive solutions for system (1.1) with η = ±1
Summary
A necessary and sufficient condition on the existence and uniqueness of positive weak solution of the system is obtained. We consider the existence and uniqueness of positive solution for the following Schrödinger–Poisson system When g(x, u) = 0, f (x) = μ is a positive parameter and 0 < γ < 1 (i.e. weak singularity), Zhang [28] obtained a sufficient condition on the existence, uniqueness and multiplicity of positive solutions for system (1.1) with η = ±1.
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