Liénard方程极限环的存在性
On the Existence of Limit Cycles of Liénard Equation
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摘要: 本文在没有常设条件G(±∞)=+∞的情况下,证明了Liénard方程存在极限环的几个充分性定理,推广了文[3~6]的某些结果.这些定理给出的条件均可估计极限环的存在区域.至少在n个极限环的充分性定理3、4的条件既不要求F(x)是奇函数,也不要求F(x)"n重互相相容"或"n重互相包含".Abstract: In this paper,we have proved several theorems which guarantee that the Liénard equation has at least one or n limit cycles without using the traditional assumption G(±∞)=+∞ Thus some results in [3-5] are extended.The limit cycles can be located by our theorems.Theorems 3 and 4 give sufficient conditions for the existence of n limit cycles having no need of the conditions that the function F(x) is odd or "nth order compatible with each other" or "nth order contained in each other".
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