  In this paper, we generalize the Picard-Fuchs equation method to study the
bifurcation of limit cycles of perturbed differential systems with two
switching lines. We obtain the detailed expression of the corresponding first
order Melnikov function which can be used to get the upper bound of the number
of limit cycles for the perturbed system by using Picard-Fuchs equation. It is
worth noting that we greatly simplify the computations and this method can be
applied to study the number of limit cycles of other differential systems with
two switching lines. Our results also show that the number of switching lines
has essentially impact on the number of limit cycles bifurcating from a period
annulus.
