On the number of limit cycles in a class of planar differential systems

Abstract

This paper investigates the number of limit cycles which can bifurcate from the periodic orbits of the
linear center $\dot{x}=y$, $\dot{y}=-x,$ when it is perturbed inside the class of all polynomial
differential systems of arbitrary degree. Using averaging theory of first and second order, we estimate
the lower bounds for the maximum number of limit cycles of these systems.