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

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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.
Multiple Solutions for Nonhomogeneous Kirchhoff-Schr?dinger-Poisson System with p-Laplacian
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.

Kirchhoff-Schrödinger-Poisson systemp-LaplacianEkeland variational principleMountain pass theorem

王梅、索洪敏、张学梅、王臣熙

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贵州民族大学数据科学与信息工程学院,贵阳,550025

Kirchhoff-Schrödinger-Poisson系统 p-Laplacian Ekeland变分原理 山路定理

National Natural Science Foundation of ChinaNational Natural Science Foundation of China

1166102111861021

2024

10.3969/j.issn.1006-8074.2024.02.002

数学理论与应用
湖南省数学学会

数学理论与应用

影响因子：0.281
ISSN：1006-8074
年,卷(期)：2024.44(2)