文章基本信息

标题：Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems
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作者：Hongxia Shi
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2019
卷号：2019
期号：1
页码：1-16
DOI：10.1186/s13661-019-1252-7
出版社：Hindawi Publishing Corporation
摘要：This paper deals with the following generalized nonhomogeneous Kirchhoff–Schrödinger–Poisson system: $$ \textstyle\begin{cases} (a+\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}+b\int _{\mathbb{R}^{3}} u ^{2} )(-\Delta u+bu)+q\phi f(u)=g(u)+h(x), & \text{in } \mathbb{R}^{3}, \\ -\Delta \phi =2q F(u), & \text{in }\mathbb{R}^{3}, \end{cases} $$ where $a>0$ , $b\geq 0$ are constants, $q\geq 0$ is a parameter, and $F(t)=\int _{0}^{t}f(s)\,\mathrm{d}s$ . Under some appropriate assumptions on $g(u)$ and $h(x)$ , the existence of two positive radial solutions is proved by applying Ekeland’s variational principle and the mountain pass theorem.
关键词：Kirchhoff;Schrödinger;Poisson systems; Variational methods; Cut-off functional; Pohozaev type identity