带有Hardy-Sobolev临界项的半线性方程基态解  

Ground State Solutions for Semilinear Equation with Hardy-Sobolev Critical Term

作　　者：郝佳鑫 黄永艳[1] HAO Jiaxin;HUANG Yongyan(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院

出　　处：《河南科技大学学报（自然科学版）》2020年第3期93-98,共6页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11571209,11671239);国家自然科学青年基金项目(11701346)

摘　　要：讨论了一类带有Hardy-Sobolev临界指数的半线性方程,在非线性项满足更一般的假设条件下,获得了该方程基态解的存在性。首先,利用变号位势的性质,得到方程对应的最小能量值为负;其次,利用变分方法,证明了该方程基态解的存在性。本文改进了有界区域上非线性项恒为常数时解的存在性结果,并将结果推广到全空间。A class of semilinear equation with Hardy-Sobolev critical exponent was discussed,and the existence of the ground state solutions for the equation was obtained when the nonlinearity term satisfied the more generally assumed conditions.Firstly,it was obtained that the least energy value corresponding to the equation was negative by using the properties of the sign-changing potential. Then,the existence of the ground state solution for the equation was proved by variational methods.The existence result of the solution was improved when the nonlinearity term permanently was constant in bounded domains,and the result was extended to the full space in the paper.

关 键 词：Hardy项 NEHARI流形 基态解 

分 类 号：O177.91[理学—数学]