带有临界指数的Kirchhoff方程最小能量变号解的存在性  

Existence of a Sign-Changing Solution with Minimal Energy for a Kirchhoff Equation with Critical Exponents

作　　者：彭秋颖 吕颖[1] PENG Qiu-ying;LU 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

出　　处：《西南师范大学学报（自然科学版）》2019年第10期23-29,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11601438)

摘　　要：研究了一类带临界指数的Kirchhoff方程-(a+b∫R3|■u|^2dx)Δu+V(x)u=h(x)|u|^p-2u+u^5x∈R^3其中a,b>0,p∈(4,6).利用Nehari流形和变分法获得了该方程的最小能量变号解.In this paper,the following Kirchhoff equation has been considered with critical exponents -(a+b∫R3|■u|^2dx)Δu+V(x)u=h(x)|u|^p-2u+u^5x∈R^3 where a,b>0,p∈(4,6).By means of Nehari manifold and variational method,the sign-changing solution with minimal energy is obtained.

关 键 词：KIRCHHOFF方程 临界指数 NEHARI流形 变分法 

分 类 号：O176.3[理学—数学]