Résumé:
We have studied continuous and discontinuous planar piecewise di erential systems formed by linear isochronous
centers and four di erent cubic isochronous centers separated by one straight line. When these piecewise di erential
systems are continuous, we have proved that they have no limit cycle, this result is stated in Theorem 3.1. On the
other hand, for discontinuous piecewise di erential systems we have shown that they provide two and one as an
upper bound on the maximum number of limit cycles for rst and second cubic systems, and three for third and
fourth cubic systems, this result is stated in Theorem 3.2. In conclusion, we have solved the extension of the 16th
Hilbert problem for these four classes of continuous and discontinuous piecewise di erential systems.
