On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

In this paper we study the maximum number N   of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies 2≤N≤42≤N≤4 if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity.