数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (4): 1064-1080.doi: 10.1007/s10473-020-0413-1

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GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR A FRACTIONAL SCHRÖ DINGER-POISSON SYSTEM WITH CRITICAL GROWTH

黄文涛, 王莉   

  1. School of Basic Science, East China Jiaotong University, Nanchang 330013, China
  • 收稿日期:2019-03-26 修回日期:2019-12-22 出版日期:2020-08-25 发布日期:2020-08-21
  • 通讯作者: Li WANG E-mail:wangli.423@163.com
  • 作者简介:Wentao HUANG,E-mail:wthuang1014@aliyun.com
  • 基金资助:
    The first author was supported by the Science and Technology Project of Education Department in Jiangxi Province (GJJ180357) and the second author was supported by NSFC (11701178).

GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR A FRACTIONAL SCHRÖ DINGER-POISSON SYSTEM WITH CRITICAL GROWTH

Wentao HUANG, Li WANG   

  1. School of Basic Science, East China Jiaotong University, Nanchang 330013, China
  • Received:2019-03-26 Revised:2019-12-22 Online:2020-08-25 Published:2020-08-21
  • Contact: Li WANG E-mail:wangli.423@163.com
  • Supported by:
    The first author was supported by the Science and Technology Project of Education Department in Jiangxi Province (GJJ180357) and the second author was supported by NSFC (11701178).

摘要: We study the following nonlinear fractional Schrödinger-Poisson system with critical growth: \begin{equation}\label{eqS0.1} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \left \{ \begin{array}{ll} (-\Delta )^s u+u+\phi u=f(u)+|u|^{2^*_s-2}u,\quad &x\in \mathbb{R}^3, \\ (-\Delta )^t \phi=u^2,& x\in \mathbb{R}^3, \\ \end{array} \right . \end{array} \end{equation} where $0 < s,t < 1$, $2s+2t > 3$ and $2^*_s=\frac{6}{3-2s}$ is the critical Sobolev exponent in $\mathbb{R}^3$. Under some more general assumptions on $f$, we prove that (0.1) admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.

关键词: fractional Schrödinger-Poisson system, Nehari-Pohozaev manifold, ground state solutions, critical growth

Abstract: We study the following nonlinear fractional Schrödinger-Poisson system with critical growth: \begin{equation}\label{eqS0.1} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \left \{ \begin{array}{ll} (-\Delta )^s u+u+\phi u=f(u)+|u|^{2^*_s-2}u,\quad &x\in \mathbb{R}^3, \\ (-\Delta )^t \phi=u^2,& x\in \mathbb{R}^3, \\ \end{array} \right . \end{array} \end{equation} where $0 < s,t < 1$, $2s+2t > 3$ and $2^*_s=\frac{6}{3-2s}$ is the critical Sobolev exponent in $\mathbb{R}^3$. Under some more general assumptions on $f$, we prove that (0.1) admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.

Key words: fractional Schrödinger-Poisson system, Nehari-Pohozaev manifold, ground state solutions, critical growth

中图分类号: 

  • 35R11