On the Existence of Ground State Solutions to a Quasilinear Schr?dinger Equation involving p-Laplacian  

作　　者：Ji-xiu WANG Qi GAO 

机构地区：[1]School of Mathematics and Statistics,Hubei University of Arts and Science,Xiangyang 441053,China [2]Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第2期381-395,共15页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (12226411);the Research Ability Cultivation Fund of HUAS (No.2020kypytd006);supported by the National Natural Science Foundation of China (11931012,11871386);the Fundamental Research Funds for the Central Universities (WUT:2020IB019)。

摘　　要：We consider the following quasilinear Schrodinger equation involving p-Laplacian-Δpu+V(x)|u|^(p-2)u-Δp(|u|^(2η))|u|^(2η-2)u=λ|u|^(q-2)u/|x|^(μ)+|u|^(2ηp*(v)-2)u/|x|^(v)in R^(N),where N>p>1,η≥p/2(p-1),p<q<2ηp^(*)(μ),p^(*)(s)=(p(N-s))/N-p,andλ,μ,νare parameters withλ>0,μ,ν∈[0,p).Via the Mountain Pass Theorem and the Concentration Compactness Principle,we establish the existence of nontrivial ground state solutions for the above problem.

关 键 词：quasilinear Schrodinger equation critical Hardy-Sobolev exponent ground state solutions SINGULARITIES 

分 类 号：O175.29[理学—数学]