带有深位势阱的薛定谔-泊松系统的多解  

Multiple solutions to Schr dinger-Poisson systems with steep potential well

作　　者：刘爽 王丽媛 毛安民[3] LIU Shuang;WANG Liyuan;MAO Anmin(Baodian Coal Mine School,273513,Zoucheng,Shandong;Gegu Third Middle School,300352,Tianjin;School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong,PRC)

机构地区：[1]邹城鲍店煤矿学校,山东省邹城市273513 [2]天津市葛沽第三中学,天津市300352 [3]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2024年第4期29-38,共10页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(12171014);山东省自然科学基金(ZR2020MA005,ZR2021MA096).

摘　　要：研究以下类型的非局部薛定谔-泊松系统:{-(a+b∫ℝ^(3)|▽u|^(2)d xΔu+λV(x)u+μФu=f(x)|u|^(q-2)u+g(x)|u|^(p-2)u,x∈ℝ^(3),-ΔФ=u^(2),x∈ℝ^(3).利用Ekeland变分原理,证明上述问题在一个球内至少存在1个正解.利用Nehari流形方法,证明上述问题在球外存在第2个解.该文结果在一定程度上推广了已有的相关结果.A class of nonlocal Schr dinger-Poisson system with steep potential well and concave-convex nonlinearities{-(a+b∫ℝ^(3)|▽u|^(2)d xΔu+λV(x)u+μФu=f(x)|u|^(q-2)u+g(x)|u|^(p-2)u,x∈ℝ^(3),-ΔФ=u^(2),x∈ℝ^(3).,is considered.By the Ekeland variational principle,one positive solution is proved to be existed in a ball^(-)B_(ρ_(0))(0).The filtration of the Nehari manifold is applied on the outside of the ball^(-)B_(ρ_(0))(0).The results in this paper extend the existing relevant results to a certain extent.

关 键 词：薛定谔-泊松系统 深位势阱 NEHARI流形 

分 类 号：O175.8[理学—数学]