临界和超临界的薛定谔泊松方程正的径向基态解  

Positive Radial Ground State Solution with Critical and Supercritical Schrödinger Poission Equation

作　　者：王玉婷 商彦英[1] WANG Yu-ting;SHANG Yang-ying(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2021年第4期20-24,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971393).

摘　　要：近些年来,薛定谔方程或者薛定谔泊松方程基态解的问题一直受到广泛关注,学者们主要讨论了不同条件下正解、基态解、变号解等的存在性问题.特别地,他们在不同的位势以及非线性项条件下研究了基态解的存在性,并且这些问题都是临界和次临界的情形,而对于临界和超临界情形下径向基态解的结果至今还没有人研究.因此,本文通过使用Nehari流形的方法,得到带有临界和超临界指数的薛定谔泊松方程正的径向基态解的存在性.In the recent years,the ground state solution of Schrödinger or Schrödinger Poisson equation has been widely concerned.Scholars mainly discussd the existence of positive solution,ground state solution and sign changing solution under different conditions.In particular,they study the existence of ground state solutions under different potentials and nonlinear term conditions,and these problems are both critical and sub-critical cases,but the existence of radial ground state solution for critical and super-critical cases have not been studied.So,in this paper,with Nehari manifold methods,we obtain the existence of radial ground states solution for the Schrödinger Poission equation with critical and super-critical nonlinear term.

关 键 词：薛定谔泊松方程 临界 超临界 NEHARI流形 强极大值原理 

分 类 号：O176.3[理学—数学]