A new Chebyshev criterion and its application to planar differential systems

阿贝尔方程中至多两个非零极限环的切比雪夫准则

A Chebyshev criterion for at most two non-zero limit cycles in Abel equations

本文提出切比雪夫准则，证明阿贝尔方程在特定条件下至多有三个极限环，改进了相关研究结果。

平面内部Radon问题中精确非唯一性的椭圆准则

An Ellipse Criterion for Exact Nonuniqueness in the Planar Interior Radon Problem

该研究刻画了平面内部Radon问题的精确非唯一性，提出椭圆准则，在同心开正方形情形得到阈值1/√2，给出了对Boman两个结论的反例。

Upper bounds for the number of limit cycles of some planar polynomial differential systems

We give an effective method for controlling the maximum number of limit cycles of some planar polynomial systems. It is based on a suitable choice of a Dulac function and the application of the well-known Bendixson-Dulac Criterion for multiple connected regions. The key point is a new approach to control the sign of the functions involved in the criterion. The method is applied to several examples.

平面哈密顿向量场周期函数的单调性：Chicone准则的推广

Monotonicity of the period function for planar Hamiltonian vector fields: A Generalization of Chicone's Criterion

本文提出了一种扩展Chicone准则的方法，用于研究平面哈密顿系统周期函数的单调性，并分析了多项式哈密顿系统中参数对周期函数单调性的影响。

重特征值意味着结点吗？一个平面微分方程问题

Repeated Eigenvalues Imply Nodes? A Problem of Planar Differential Equations

本文针对平面微分方程中Poincaré平衡点形状判定准则在重特征值情形下的失效问题，给出了$C^1$反例，并证明将条件加强至$C^{1,α}$时该断言依然成立。

阿贝尔方程与平面系统的极限环唯一性

Uniqueness of Limit Cycles for Abel Equations and Planar Systems

该研究针对$2\pi$周期系数的阿贝尔方程，提出半周期凸性方法证明其正极限环的唯一性与双曲性，并将结果应用于两类平面多项式系统，解答了Gasull公开问题的部分内容。