Existence, uniqueness and multiplicity of positive solutions for Schrödinger-Poisson system with singularity

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• 作者：Qi Zhang ; ^{zhangqi@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Schrö ; dinger&ndash ; Poisson system ; Singularity ; Uniqueness ; Multiplicity
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：437
• 期：1
• 页码：160-180
• 全文大小：420 K

文摘

In this paper, we consider the following Schrödinger–Poisson system with singularity where Ω⊂R³$\mathrm{\Omega }\subset {\mathbb{R}}^3$ is a smooth bounded domain with boundary ∂Ω, 41125bc28f1a8d863bb0ba8f" title="Click to view the MathML source">η=±1$\eta =\pm 1$, r∈(0,1)$r\in (0,1)$ is a constant, μ>0$\mu >0$ is a parameter. We obtain the existence and uniqueness of positive solution for η=1$\eta =1$ and any μ>0$\mu >0$ by using the variational method. The existence and multiplicity of solutions for the system are also considered for η=−1$\eta =-1$ and μ>0$\mu >0$ small enough by using the method of Nehari manifold.