題  目：The number of limit cycles of Josephson equation

内容簡介：In this talk, we will study the Josephson equations，which can be transformed the following Lienard systems on the cylinder: x’(t)=y, y’(t)=-(sin x-a)-(b+c cos x)y. We concern the non-contractible limit cycles, which are the isolated 2\pi-periodic solutions y=y(x). This problem is equivalent to study the non-zero limit cycles of the following Abel equations y’(x)=（b+cos x）y^2-(sin x-a) y^3. By the theory of rotation vectors and studying the multiplicity of limit cycles, we will show that at most two non-zero limit cycles can appear. Our work can be also viewed as a step to solve the following open problem: Open problem: y’(x)=(a_0+a_1 sin x+a_2 cos x)y^3+(b_0+b_1 sin x+b_2 cos x)y^2 have at most three limit cycles (The trivial limit cycle y=0 is included). This is a joint work with Xiangqin Yu and Hebai Chen.

報告人：劉長劍  教授

報告人簡介：中山大學數學學院（珠海）教授。本、碩、博均畢業于北京大學，并獲北京大學-裡爾第一大學聯合培養博士學位。主要從事常微分方程與動力系統方面的研究，在Trans. AMS, JDE, Nonlinearity 等雜志發表論文40餘篇，主持多項國家自然科學基金面上項目。

時  間：2023年5月4日（周四）上午 10：00 始

地  點：太阳集团app首页番禺校區 教學樓 N421

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