Stability analysis of Abel's equation of the first kind

Abstract

This paper established sufficient conditions for the stability of Abel's differential equation of the first kind. These conditions explicate the impact of the asymptotic behaviors exhibited by the time-varying coefficients on the overall stability of the system. More precisely, we studied the positivity, the continuation and the boundedness of solutions. Additionally, we investigated the attractivity, the asymptotic stability, the uniform stability and the instability of the system. The results were scrutinized by numerical simulations.

Keywords

• abel's equation
• attractivity
• asymptotic stability
• uniform stability
• boundedness of solutions