On the lymit cicles of discontinuous piecewise linear differentuial systems formed by centers and separated by irreducible cubic curves III

In this paper we provide a lower bound for the maximum number of crossing limit cycles of some class of planar discontinuous piecewise linear differential systems formed by centers and separated by an irreducible algebraic cubic curve. More precisely we study the existence of simultaneous crossing limit cycles with four and two intersection points with the cubic of separation. In previous papers [3, 4] we already have studied the lower bounds for the maximum number of crossing limit cycles when these limit cycles only have either four or two intersection points with the cubic of separation..