Multiplicity and Concentration of Positive Solutions for a Quasilinear Schrödinger-Poisson System with Critical Nonlinearity  

临界的拟线性Schrödinger-Poisson系统正解的多重性和集中性

作　　者：ZHANG Weiqiang WEN Yanyun 张伟强;温彦云(甘肃民族师范学院数学科学学院,合作747000)

机构地区：[1]School of Department of Mathematics,Gansu Normal College For Nationalities,Hezuo 747000,China

出　　处：《数学理论与应用》2025年第1期1-24,共24页Mathematical Theory and Applications

基　　金：supported by the Natural Science Foundation of Gansu Province(No.24JRRP001)。

摘　　要：In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R is a potential function with a local minimum and f is subcritical growth.Based on the penalization method,Nehari manifold techniques and Ljusternik-Schnirelmann category theory,we obtain the multiplicity and concentration of positive solutions to the above system.本文考虑以下薛定谔-泊松系统{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p),其中ε>0是一个参量,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R是满足局部极小条件的位势,f是次临界增长的.基于罚方法、Nehari流形技巧和Ljusternik Schnirelmann畴数理论,我们得到正解的多重性和集中性.

关 键 词：Schrödinger-Poisson system Positive solution Ljusternik-Schnirelmann category theory Critical growth P-LAPLACIAN 

分 类 号：O175.25[理学—数学]