一类p-Laplacian的非齐次Kirchhoff-Schrödinger-Poisson系统的多重解研究  

Multiple Solutions for Nonhomogeneous Kirchhoff-Schrödinger-Poisson System with p-Laplacian

作　　者：王梅 索洪敏 张学梅 王臣熙 Wang Mei;Suo Hongmin;Zhang Xuemei;Wang Chenxi(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《数学理论与应用》2024年第2期20-35,共16页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China(Nos.11661021,11861021)。

摘　　要：本文考虑如下p-Laplacian的非齐次拟线性Kirchhoff-Schr?dinger-Poisson系统解的存在性:{-(a-b∫_(R^(3))|■u|^(p)dx)△_(p)u+|u|^(p-2)u+λφ_(u)u=|u|^(q-2)u+h(x),x∈R^(3),-△_(φ)=u^(2),其中a,b>0,4/3<p<12/5,p<q<p^(*)=3p/3-p,λ>0.当h(x)满足适当的条件时,运用Ekeland变分原理和山路定理给出系统多重解的存在性.In this paper we consider the existence of solutions to the nonhomogeneous quasilinear Kirchhoff-Schr?dinger-Poisson system with p-Laplacian:{-(a-b∫_(R^(3))|■u|^(p)dx)△_(p)u+|u|^(p-2)u+λφ_(u)u=|u|^(q-2)u+h(x),x∈R^(3),-△_(φ)=u^(2),where a,b>0,4/3<p<12/5,p<q<p^(*)=3p/3-p,λ>0.Under suitable assumptions on h(x),the existence of multiple solutions of the system is obtained by using the Ekeland variational principle and the Mountain pass theorem.

关 键 词：Kirchhoff-Schrödinger-Poisson系统 P-LAPLACIAN EKELAND变分原理 山路定理 

分 类 号：O175[理学—数学]