The existence and multiplicity of solutions of a fractional Schrdinger-Poisson system with critical growth

作     者：Yuanyang Yu Fukun Zhao Leiga Zhao 

作者机构：Department of Mathematics Yunnan Normal University Kunming 650500 China Department of Mathematics Beijing University of Chemical Technology Beijing 100029 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2018年第61卷第6期

页      面：1039-1062页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11361078 and 11661083) 

主　　题：fractional Schrodinger-Poisson system critical growth variational methods 

摘      要：In this paper, we study the existence and multiplicity of solutions for the following fractional Schrodinger-Poisson system：（{ε2S（-△）Su＋V（x）u＋φu=｜u｜2＊s-2＋f（u）in R3ε2s（-△）sφ=u in R3（0.1）where 3/4〈s〈1,2＊：＋6/3-2s）is the fractional critical exponent for 3-dimension, the potential V ： R3→ R is continuous and has global minima, and f is continuous and supercubic but subcritical at infinity. We prove the existence and multiplicity of solutions for System （0.1） via variational methods.