中北大学学报（自然科学版）2016，Vol.37Issue(6)：576-580,5.DOI:10.3969/j.issn.1673-3193.2016.06.005
R3双临界Kirchhoff型方程正解的存在性
Existence of Positive Solutions for Kirchhoff Type Problems in R3 with Multiple Critical Nonlinearities
宋雅倩 1张福伟 1刘进生1
作者信息
- 1. 太原理工大学 数学学院，山西 太原 030024
- 折叠
摘要
Abstract
The existence of positive solutions for Kirchhoff type problem with multiple critical nonlineari-ties was investigated by using variational method.Firstly,it was proved that the energy functional pos-sessed mountain pass geometry and got a (PS)c sequence.Then,it was demonstrated that the (PS)c se-quence contained strong convergent subsequence through the boundedness of the (PS)c sequence,the non triviality of weak limit,and the property of radial symmetry space.Therefore,the energy functional has at least one nontrivial critical point and the problem has at least one nontrivial solution.Consequent-ly,it is achieved that the nontrivial solution is positive.关键词
Kirchhoff型方程/双临界非线性项/山路引理/正解Key words
Kirchhoff type problem/multiple critical nonlinearities/mountain pass theorem/positive so-lution分类
数理科学引用本文复制引用
宋雅倩,张福伟,刘进生..R3双临界Kirchhoff型方程正解的存在性[J].中北大学学报（自然科学版）,2016,37(6):576-580,5.
