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Bifurcation of limit cycles in a class of piecewise smooth generalized Abel equations with two asymmetric zones
Haihua Liang, Jianfeng Huang
This paper studies the number of limit cycles, known as the Smale-Pugh problem, for the generalized Abel equation \begin{align*} \frac{dx}{dθ}=A(θ)x^p+B(θ)x^q, \end{align*} where $…
A new Chebyshev criterion and its application to planar differential systems
Jianfeng Huang, Haihua Liang, Xiang Zhang
This paper establishes a new Chebyshev criterion for some family of integrals. By virtue of this criterion we obtain several new Chebyshev families. With the help of these new fami…
Limit cycles of planar system defined by the sum of two quasi-homogeneous vecter fields
Jianfeng Huang, Haihua Liang
In this paper we consider the limit cycles of the planar system where and are quasi-homogeneous vector f…
A geometric criterion for equation having at most isolated periodic solutions
Jianfeng Huang, Haihua Liang
This paper is devoted to the investigation of generalized Abel equation , where . A solution is called…