一类p-Laplacian的非齐次Kirchhoff-Schr?dinger-Poisson系统的多重解研究
Multiple Solutions for Nonhomogeneous Kirchhoff-Schr?dinger-Poisson System with p-Laplacian
王梅 1索洪敏 1张学梅 1王臣熙1
作者信息
- 1. 贵州民族大学数据科学与信息工程学院,贵阳,550025
- 折叠
摘要
本文考虑如下p-Laplacian的非齐次拟线性Kirchhoff-Schrödinger-Poisson系统解的存在性:{-(a-b ∫R3|▽u|pdx)Δpu+|u|p-2u+λφuu=|u|q-2u+h(x),x ∈ R3,-Δφ=u2,x ∈ R3,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.
Abstract
In this paper we consider the existence of solutions to the nonhomogeneous quasilinear Kirchhoff-Schrödinger-Poisson system with p-Laplacian:{-(a-b ∫R3|▽u|pdx)ΔpU+|u|p-2 u+λφuu=|u|q-2u+h(x),x ∈ R3,{-Δφ=u2,x ∈ R3,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Key words
Kirchhoff-Schrödinger-Poisson system/p-Laplacian/Ekeland variational principle/Mountain pass theorem引用本文复制引用
基金项目
National Natural Science Foundation of China(11661021)
National Natural Science Foundation of China(11861021)
出版年
2024
NETL
NSTL
万方数据