CAJ | 학술논문

本文讨论了一类非Liénard型三次系统的极限环问题.首先对二次系统情况我们给出了补充中心充要条件的一个例子.其次将此系统化成Liénard系统后设法证明了极限环的惟一性.最后利用广义Hopf分支定理说明此系统可具有两个极限环.
본문토론료일류비Liénard형삼차계통적겁한배문제.수선대이차계통정황아문급출료보충중심충요조건적일개례자.기차장차계통화성Liénard계통후설법증명료겁한배적유일성.최후이용엄의Hopf분지정리설명차계통가구유량개겁한배.
In this paper we discuss the limit cycle problem for a non-Liénard type cubic system. Firstly for quadratic case, we find an example to show the sufficiency about the center conditions. Secondly we prove the uniqueness of limit cycles by translating the system to Liénard type and by using the related uniqueness theorem of limit cycles. Lastly we show that the cubic system may have at least two limit cycles by using the generalized Hopf bifurcation theorem.