  In this paper, we establish a unilateral global bifurcation result for a
class of quasilinear periodic boundary problems with a sign-changing weight. By
the Ljusternik-Schnirelmann theory, we first study the spectrum of the periodic
$p$-Laplacian with the sign-changing weight. In particular, we show that there
exist two simple, isolated, principal eigenvalues $\lambda_0^+$ and
$\lambda_0^-$. Furthermore, under some natural hypotheses on perturbation
function, we show that $(\lambda_0^\nu,0)$ is a bifurcation point of the above
problems and there are two distinct unbounded sub-continua
$\mathscr{C}_\nu^{+}$ and $\mathscr{C}_\nu^{-}$, consisting of the continuum
$\mathscr{C}_\nu$ emanating from $(\lambda_0^\nu, 0)$, where $\nu\in\{+,-\}$.
As an application of the above result, we study the existence of one-sign
solutions for a class of quasilinear periodic boundary problems with the
sign-changing weight. Moreover, the uniqueness of one-sign solutions and the
dependence of solutions on the parameter $\lambda$ are also studied.
