达布多项式及其相关性质  

Darboux Polynomials and Its Related Properties

作　　者：沈彩霞[1] 

机构地区：[1]河池学院数学系,广西宜州546300

出　　处：《钦州学院学报》2008年第3期24-25,33,共3页Journal of Qinzhou University

基　　金：广西教育厅科学研究项目(200707MS112);广西教育厅科学研究项目(200707LX324)

摘　　要：达布多项式与首次积分有密切联系,而且达布多项式存在性条件比首次积分存在性条件弱得多,故利用达布多项式寻找多项式系统的首次积分(或由达布多项式的不存在性证明首次积分的不存在性)有积极意义.Darboux polynomials and first integrals have close relation, the conditions for the existence of a Darboux polynomial are much weaker than the conditions for the existence of a fist integral, it is positive meaning that we use Darboux polynomials to find out first integrals of the polynomial system or use the nonexistence of Darboux polynomials to prove the nonexistence of first integrals. The essay shows Darboux polynomials related properties and detailed proof.

关 键 词：达布多项式 首次积分 导数 

分 类 号：O175[理学—数学]