Upper bounds of limit cycles in Abel differential equations with invariant curves

TL;DR

This paper develops new criteria to determine upper bounds on the number of limit cycles in Abel differential equations with invariant curves, aiding the analysis of planar differential systems.

Contribution

It introduces novel criteria for bounding limit cycles in Abel differential equations with invariant curves, especially when one curve is bounded.

Findings

Upper bounds of zero or one limit cycle established for certain systems

Criteria applicable to planar differential systems

Enhanced understanding of limit cycle behavior in Abel equations

Abstract

New criteria are established for upper bounds on the number of limit cycles of periodic Abel differential equations having two periodic invariant curves, one of them bounded. The criteria are applied to obtain upper bounds of either zero or one limit cycle for planar differential systems.