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In this paper, we study the number of limit cycles that can bifurcating froma periodic annulus in discontinuous planar piecewise linear Hamiltoniandifferential system with three zones separated by two parallel straight lines.We prove that if the central subsystem, i.e. the system defined between the twoparallel lines, has a real center and the others subsystems have centers orsaddles, then we have at least three limit cycles that appear afterperturbations of periodic annulus. For this, we study the number of zeros of aMelnikov function for piecewise Hamiltonian system and present a normal formfor this system in order to simplify the computations.

Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian differential System with Three Zones