一类耦合系统的无穷多共振解  

Infinitely Many Resonant Solutions for a Class of System

作　　者：魏其萍 王跃 熊宗洪 郝雪妍 WEI Qiping;WANG Yue;XIONG Zonghong;HAO Xueyan(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025;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,贵阳550025 [2]贵州大学数学与统计学院,贵阳550025

出　　处：《重庆师范大学学报（自然科学版）》2021年第2期63-69,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11661021);贵州省研究生科研基金(No.黔教合YJSCXJH[2020]083);贵州省科技厅科技计划联合基金(No.黔科合LH字[2014]7378);贵州省教育厅青年人才项目(No.黔教合KY字[2017]318,No.黔教合KY字[2018]141,No.黔教合KY字[2018]415)。

摘　　要：【目的】考虑含有线性项的基尔霍夫型耦合系统无穷多解的存在性。【方法】利用本征值问题相关理论和代数分析方法进行求解。【结果】获得无穷多经典解,在实际应用中它们表现出共振形态。【结论】每一个扰动函数至少对应一个共振解,系统中的参数满足不同条件时分别有1族、2族或3族解,并且通过实例验证了结果的可靠性。[Purposes]Consider the existence of infinitely many solutions for a Kirchhoff-type coupled system with linear terms.[Methods]It is discussed by using the theories of eigenvalue problem and the method of algebraic analysis.[Findings]It obtains that there are infinitely many classical solutions,which show resonance in practical applications.[Conclusions]It is shown that the system has at least a class of resonant solutions.By the way,there are one,two or three classes of solutions when the parameters satisfy different conditions in the system.Moreover,an example is given to supplement the conclusions drawn.

关 键 词：基尔霍夫型问题 耦合系统 共振解 代数分析方法 

分 类 号：O231[理学—运筹学与控制论] O177[理学—数学]