Normalized Solutions for p-Laplacian Schrödinger-Poisson Equations with L^(2)-Supercritical Growth  

具有L^(2)超临界增长的p-Laplacian Schrödinger-Poisson方程的正规化解

作　　者：LI Mingxue ZHANG Jiafeng 李明雪;张家锋(贵州民族大学数据科学与信息工程学院,贵阳550025)

机构地区：[1]School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China

出　　处：《数学理论与应用》2025年第1期45-61,共17页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China(No.12461024);the Natural Science Research Project of Department of Education of Guizhou Province(Nos.QJJ2023012,QJJ2023061,QJJ2023062);the Natural Science Research Project of Guizhou Minzu University(No.GZMUZK[2022]YB06)。

摘　　要：In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a Lagrange multiplier.We obtain the critical point of the corresponding functional of the problem on mass constraint by the variational method and the Mountain pass lemma,and then find a normalized solution to this equation.本文研究如下具有L^(2)质量的p-Laplacian Schrödinger-Poisson方程-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),其中2≤p<3,5p/3*=3p/3-p,λ>0是拉格朗日乘子.我们利用变分法和山路引理找到该问题在规定质量上对应泛函的临界点,从而得到方程有一个正规化解.

关 键 词：Normalized solution p-Laplacian equation Schrödinger-Poisson equation Mountain pass lemma 

分 类 号：O175.25[理学—数学]