Periodic Solutions of Abel Differential Equations

2006/05/05 by M.A.M. Alwash, Alwash, M. A. M.
Mathematics · Medicine · Physics and Astronomy · #34C #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.math/0605153

openalex publication_date 2006/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation.

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