【摘要】 该文的目的是给出一般非线性系统存在和部分存在有理首次积分的判别准则.作者给出系统存在有理首次积分的必要条件,在此基础上进一步给出系统不存在其它有理首次积分(在函数独立的意义下)的判定准则.更多还原

【Abstract】 The objective of this paper is to present some criteria for nonexistence and partial existence of rational first integrals for general nonlinear systems.The author first gives a necessary condition for general nonlinear systems to having rational first integrals.Then the author considers the case that the system have owed some rational integrals.Under certain conditions,the author proves that the system does not admit any other rational first integrals in the sense of functional independence,and thus the system is partially integrable.更多还原