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Multiplicity and concentration of positive solutions for the fractional Schrödinger-Poisson systems with critical growth

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成果类型:
期刊论文
作者:
Liu, Zhisu*;Zhang, Jianjun
通讯作者:
Liu, Zhisu
作者机构:
[Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
[Zhang, Jianjun] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China.
[Zhang, Jianjun] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China.
通讯机构:
[Liu, Zhisu] U
Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
语种:
英文
关键词:
Critical growth;Fractional Schrödinger-Poisson system;Positive solution;Variational method
期刊:
ESAIM: Control, Optimisation and Calculus of Variations
ISSN:
1292-8119
年:
2017
卷:
23
期:
4
页码:
1515-1542
基金类别:
Acknowledgements. The authors would like to express their sincere gratitude to the anonymous referee for carefully reading the manuscript, giving valuable comments and suggestions to improve the results as well as the exposition of the paper. Z. Liu was supported by Science and Technology Development Project of Hengyang City(2016KJ59); J. Zhang was supported by the Science Foundation of Chongqing Jiaotong University(15JDKJC-B033).
机构署名:
本校为第一且通讯机构
院系归属:
数理学院
摘要:
In this paper, we study the multiplicity and concentration of solutions for the following critical fractional Schrödinger–Poisson system: \begin{eqnarray*} \left\{ \begin{array}{ll} \epsilon^{2s}(-\triangle)^{s} {u}+ V(x)u+\phi u =f(u)+|u|^{2^*_{s}-2}u &\mbox{in}\,\,\R^3, \\[2.5mm] \epsilon^{2t}(-\triangle)^{t}{\phi}=u^2 &\mbox{in}\,\, \R^3, \end{array} \right. \end{eqnarray*} where ϵ> 0 is a small parameter, (− △ )α denotes the fractional Laplacian of order α = s,t ∈ (0,1), where 2α∗6/3−2α is the fractional critical exponent in Dim...

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