On the existence of limit cycles of the equation \(x'=h(y)-F(x),y'=-g(x)\). (English) Zbl 0689.34026
This paper is concerned with the following generalization of the Lienard equation \(\dot x=h(y)-f(x),\) \(\dot y=-g(x).\) After a number of preparatory lemmas, three main theorems are given. They assert that, under stated assumptions, there exists at least one limit cycle of the system. The method of proof relies on the construction of a suitable Poincaré-Bendixson annular region.
Reviewer: E.O.Roxin
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
References:
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