一类耦合系统的解及共振  

Solutions and their resonances to a coupled systems

作　　者：魏其萍 王跃 WEI Qiping;WANG Yue(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang,Guizhou 550025,China;School of Mathematics and Statistics,Guizhou University,Guiyang,Guizhou 550025,China)

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

出　　处：《湖南城市学院学报（自然科学版）》2021年第4期49-55,共7页Journal of Hunan City University:Natural Science

基　　金：国家自然科学基金项目(11661021);贵州省研究生科研基金项目(黔教合YJSCXJH[2020]083)。

摘　　要：考虑了1类基尔霍夫方程的耦合系统,利用代数分析方法获得了其解的存在性和多重性,并结合实际背景,对系统及其解的物理意义进行了阐述.研究表明,当参数满足不同的取值区间时,系统分别存在n对、不少于n对或3n对解,这些解在日常应用中呈现为共振形态.In this paper,the coupled system of a kind of Kirchhoff equation is considered,and the existence and multiplicity of the solution are obtained by using the algebraic analysis method.Combined with the practical background,the physical meaning of the system and its solution are expounded.The results show that there are n pairs,not less than n pairs or 3n pairs of solutions in the system when the parameters meet different value intervals,and these solutions show a resonant form in daily applications.

关 键 词：基尔霍夫方程 耦合系统 代数分析方法 共振解 

分 类 号：O175.23[理学—数学]