  In this paper, we study limit cycle bifurcations for a kind of non-smooth
polynomial differential systems by perturbing a piecewise linear Hamiltonian
system with a center at the origin and a homoclinic loop around the origin. By
using the first Melnikov function of piecewise near-Hamiltonian systems, we
give lower bounds of the maximal number of limit cycles in Hopf and homoclnic
bifurcations, and derive an upper bound of the number of limit cycles that
bifurcate from the periodic annulus between the center and the homoclinic loop
up to the first order in. In the case when the degree of perturbing terms is
low, we obtain a precise result on the number of zeros of the first Melnikov
function.
