中北大学学报（自然科学版）2016，Vol.37Issue(5)：441-445,5.DOI:10.3969/j.issn.1673-3193.2016.05.001
R3上一类Kirchhoff型方程组正解的存在性
Existence of Positive Solutions for a Kind of Kirchhoff-Type System in R3
梁静 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 with a kind of typical nonlinear Kirchhoff-type systems in R3 was investigated by using variational methods.Firstly,The corresponding energy functional in the appropriate space of this problem was given,then the desired solutions were equivalent to the critical points of the energy functional.Secondly,it is proved that the energy functional possessed the mountain pass geometry.Thus,a (PS)c sequence of the energy functional I was obtained.Meanwhile,the boundedness of the (PS)c sequence was demonstrated.Then,the (PS)c sequence had a convergent sub-sequence,that is to say,the (PS)c sequence satisfied (PS)c condition.Therefore,there existed at least one nontrivial nonnegative critical point (u,v)for the energy functional by using Mountain Pass Lemma. Finally,it is proved that u>0 and v>0 under certain assumptions.Consequently,there is at least one positive solution for the systems.关键词
Kirchhoff型方程组/变分方法/正解Key words
Kirchhoff-type systems/variational methods/positive solutions分类
数理科学引用本文复制引用
梁静,张福伟,刘进生..R3上一类Kirchhoff型方程组正解的存在性[J].中北大学学报（自然科学版）,2016,37(5):441-445,5.
