On the limit cycles for a class of generalized Liénard differential systems

The main aim of the present paper is to study the existence of limit cycles (i.e. close trajectories in the phase space having the property that at least one other trajectory spirals into them either as time approaches infinity or as time approaches negative infinity) of a class of piecewise generalized Liénard differential system modulated by a two variable polynomial and a piecewise linear function respectively. The main tool that we use to obtain these results is the averaging theory of the dynamical systems worthy to detect the initial conditions of the birth of isolated orbits of a system.