一类Kirchhoff型弱耦合系统的多重解的存在性  

Existence of multiple solutions for a kind of coupled systems with Kirchhoff-type

作　　者：魏其萍 王跃 熊宗洪 王守财 Wei Qiping;Wang Yue;Xiong Zonghong;Wang Shoucai(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025 [2]贵州大学数学与统计学院,贵州贵阳550025

出　　处：《湖南文理学院学报（自然科学版）》2021年第3期1-4,11,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：国家自然科学基金项目(11661021);贵州省研究生科研基金立项项目(YJSCXJH[2020]083);贵州省教育厅青年科技人才成长项目(黔教合KY字[2017]318号);贵州省教育厅科研项目(黔教合KY字[2018]141,黔教合KY字[2018]415号)。

摘　　要：使用代数分析技巧研究一类含线性项的非退化与退化情形弱耦合的Kirchhoff型系统,得到无穷多解的同时对解的关联性质进行了分析,总结出参数在3个不同取值区间时该问题至少有m+1对、m+2对或3m对共振解。A kind of Kirchhoff-type system with linear terms and degeneration weakly coupled non degenerate case is researched by using the technique of algebraic analysis,and the infinitely many solutions are obtained and the relationship between those solutions are analyzed.As a result,it is summarized that the system has at least m+1,m+2 or 3m pairs of resonant solutions when the parameter satisfies the different value ranges.

关 键 词：Kirchhoff型系统 弱耦合系统 代数分析技巧 

分 类 号：O231[理学—运筹学与控制论] O177[理学—数学]