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

作     者：Ji-xiu WANG Qi GAO Ji-xiu WANG;Qi GAO

作者机构：School of Mathematics and StatisticsHubei University of Arts and ScienceXiangyang 441053China Department of MathematicsSchool of ScienceWuhan University of TechnologyWuhan 430070China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2023年第39卷第2期

页      面：381-395页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：quasilinear Schrodinger equation critical Hardy-Sobolev exponent ground state solutions singularities 

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 Np1,η≥p/2(p-1),p0,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.