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 assmuption G(±∞) =+∞. Thus some results in [3–5] are extended. The limit cycles can he 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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An-ji, H., Deng-qing, C. On the existence of limit cycles of Liénard equation. Appl Math Mech 11, 125–138 (1990). https://doi.org/10.1007/BF02014537
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DOI: https://doi.org/10.1007/BF02014537