一类耦合系统的解及共振

Solutions and their resonances to a coupled systems

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.