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.
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)。
