  This paper studies the family of piecewise linear differential systems in the
plane with two pieces separated by a switching curve $y=x^{m}$, where $m>1$ is
an arbitrary positive. By analysing the first order Melnikov function, we give
an upper bound and an lower bound of the maximum number of limit cycles which
bifurcate from the period annulus around the origin under polynomial
perturbations of degree $n$. The results shows that the degree of switching
curves affect the number of limit cycles.
