具有不定位势的薛定谔-泊松系统多重解的存在性  

Existence of multiple solutions of Schr dinger-Poisson system with indefinite potential

作　　者：肖琳炼 袁家倩 周鉴 XIAO Linlian;YUAN Jiaqian;ZHOU Jian(School of Mathematical Sciences,Guizhou Normal University,550025,Guiyang,Guizhou,PRC)

机构地区：[1]贵州师范大学数学科学学院,贵州省贵阳市550025

出　　处：《曲阜师范大学学报(自然科学版)》2025年第2期59-65,共7页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(12161019);贵州师范大学博士科研基金(GZUNUD[2019]14).

摘　　要：研究一类具有不定位势的薛定谔-泊松系统{-Δu+V(x)u+∅u=f(x,u),x∈ℝ^(3),-Δ∅=u^(2),x∈ℝ^(3)多重解的存在性,其中位势函数V(x)是可变号的.当f满足适当的条件时,利用对称山路定理得到了该系统无穷多解的存在性.In this paper,the existence of infinitely many nontrivial solutions for the following nonlinear Schr dinger-Poisson system{-Δu+V(x)u+∅u=f(x,u),x∈ℝ^(3),-Δ∅=u^(2),x∈ℝ^(3) is studied,where the potential V(x)is allowed to be sign-changing.Under some suitable assumptions on f,the existence of infinitely many solutions via the symmetric mountain pass theorem is eslablished.

关 键 词：薛定谔-泊松系统 (C)_(c)条件 对称山路定理 

分 类 号：O177.91[理学—数学]