A note on ''uniqueness of limit cycles in a Lienard-type system''

[摘要] Huang and Sun [J. Math. Anal. Appl. 184 (1994), 348-359] proposed a theorem to guarantee the uniqueness of limit cycles for the generalized Lienard system dx/dt = h(y) - F(x), dy/dt = - g(x). We will give a counterexample to their theorem. It will be shown that their theorem is valid only if F(x) is monotone on certain intervals. For this case we give a shorter proof and we also show that the limit cycle is hyperbolic. If the condition on the monotonicity of F(x) is violated then we need an additional condition to guarantee the uniqueness of the limit cycle. Examples are provided to illustrate our results. (C) 1997 Academic Press.

[发布日期] 1997-04-01