勷勤数学•专家报告

题      目：Bifurcation of Limit Cycles in a Class of Piecewise Smooth Generalized Abel Equations with Two Asymmetric Zones

报  告  人：梁海华  教授  (邀请人：喻洪俊)

                                  广东技术师范大学

时      间：10月24日  16：00-17：00

地     点：学院西楼二楼会议室

报告人简介:

       梁海华，男，博士，广东技术师范大学教授、硕士生导师，中国数学会奇异摄动专委会委员，广东省工业与应用数学学会常务理事，广东省本科高校数学类专业教学指导委员会委员。2010年毕业于中山大学应用数学专业，获理学博士学位。研究方向为常微分方程定性、稳定性、分支理论、边值问题及其应用。以第一作者或通讯作者在SCI数学期刊发表学术论文30多篇，所发表的期刊包括《Journal of Differential Equations》《Discrete and Continuous Dynamical Systems》《Science China Mathematics》等。主持了3项国家自然科学基金项目、3项广东省自然科学基金项目和2项厅级重点科研项目。获广东省自然科学二等奖（第二完成人）、广东技术师范大学教学成果一等奖、广东技术师范大学教学名师奖。

摘      要：

       This paper studies the number of limit cycles, known as the Smale-Pugh problem, for a class of the generalized Abel equation
with the coefficient $A$ and $B$ being piecewise trigonometrical polynomials of degree $ m $ with two zones sperated by $ \theta= \theta_1$. By means of the first and second order analysis using the Melnikov theory and applying the new Chebyshev criterion, we estimate the maximum number of positive and negative limit cycles that such equations can have, and reveal how this maximum number is affected by the location of the separation line $\theta=\theta_1$. For the equation of classical Abel type, our result not only includes the known estimates, but also shows that the equation in the discontinuous case can possess more than two times as many limit cycles as in the continuous case.

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