Periodic solutions of polynomial non-autonomous differential equations

Abstract

We present some results on the number of periodic solutions for scalar non-autonomous polynomial equations of degree five. We also consider a class of polynomial equations of any degree. Our results give upper bounds for the number of limit cycles of two-dimensional systems.

Keywords

• Periodic solutions
• polynomial non-autonomous equations
• Abel differential equations
• limit cycles
• uniformly isochronous centers
• Hilbert's sixteenth problem.