临界或超临界增长分数阶Schrodinger-Poisson方程正解的存在性  

Existence of Positive Solutions for Fractional Schrodinger-Poisson System with Critical or Supercritical Growth

作　　者：王文波 周见文[1] 李永昆[1] 李全清 Wen Bo WANG;Jian Wen ZHOU;Yong Kun LI;Quan Qing LI(School of Mathernatics and Statistics,Yunnan University,Kunming 650500,P.R.China;Department of Mathematics,Honghe University,Mengzi 661100,P.R.China)

机构地区：[1]云南大学数学与统计学院,昆明650500 [2]红河学院数学学院,蒙自661100

出　　处：《数学学报（中文版）》2021年第2期269-280,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11901514,11861072,11961078,11561072,11801153)。

摘　　要：本文研究如下分数阶Schrodinger-Poisson方程{(-△)^(s)u+Vx(u)+K(x)φu=f(u)+λ|u|^(q-2)ux∈R^(3),(-△)^(t)φ=K(x)u^(2),x∈R^(3)其中S∈(3/4,1),t∈(0,1),f是在原点超线性无穷远次临界的连续非线性项,指数q≥2_(s)^(*)=6/3-2x.当λ>0充分小时,我们利用变分方法证明上述问题正解的存在性.本文的主要贡献是处理了超临界情形.We study the following fractional Schrodinger-Poisson system{(-△)^(s)u+Vx(u)+K(x)φu=f(u)+λ|u|^(q-2)ux∈R^(3),(-△)^(t)φ=K(x)u^(2),x∈R^(3),where S∈(3/4,1),t∈(0,1),the continuous function/is superlinear at zero and subcritical at infinity and the exponent q≥2_(s)^(*)=6/3-2x.We obtain a positive solution of the above problem for smallλ>0 via the variational method.Our main contribution is that we can deal with the supercritical case.

关 键 词：分数阶Schrodinger-Poisson方程 临界或超临界增长 Moser迭代 

分 类 号：O175.29[理学—数学]