非线性振动方程周期解的存在性

THE EXISTENCE OF LIMIT CYCLES OF NONLINEAR OSCILLATORY DIFFERENTIAL EQUATIONS

构造了Ｐｏｉｎｃａｒｅ－Ｂｅｎｄｉｘｓｏｎ环域，证明了非线性振动方程ｘ¨＋ｆ（ｘ）ｘ·＋ｇ（ｘ）＝０及ｘ¨＋（ｆ（ｘ）＋ｇ（ｘ）ｘ·）ｘ·＋ｈ（ｘ）＝０的极限环的存在性，其中ｆ（ｘ），ｇ（ｘ），ｈ（ｘ）在（－∞。

By constructing a suitable Poincare Bendixson annular region, this paper proves the existence of limit cycles of the following nonlinear oscillatory differential equations: x¨+f(x)x·+g(x)=0 and x¨+(f(x)+g(x)x·)x·+h(x)=0 where f(x), g(x) and h(x) are continueous on (-∞, +∞).