Crossing Limit Cycles from Discontinuous Piecewise Linear Differential Centers Separated by Two Circles

In recent years, there has been growing interest in the study of planar discontinuous piecewise differential systems due to their significant applications in modeling real-world phenomena. Understanding the dynamics of these systems presents several challenges, particularly in the investigation of their limit cycles. In this work, we study the existence of crossing limit cycles in discontinuous planar piecewise differential systems formed by linear centers and separated by two concentric circles. We prove that the upper bound for the number of limit cycles for this class of systems is 2 and provide examples showing that the maximum number of limit cycles can be reached.