  In this paper, we shall establish a Dancer-type unilateral global bifurcation
result for a class of quasilinear elliptic problems with sign-changing weight.
Under some natural hypotheses on perturbation function, we show that
$(\mu_k^\nu(p),0)$ is a bifurcation point of the above problems and there are
two distinct unbounded continua, $(\mathcal{C}_{k}^\nu)^+$ and
$(\mathcal{C}_{k}^\nu)^-$, consisting of the bifurcation branch
$\mathcal{C}_{k}^\nu$ from $(\mu_k^\nu(p), 0)$, where $\mu_k^\nu(p)$ is the
$k$-th positive or negative eigenvalue of the linear problem corresponding to
the above problems, $\nu\in\{+,-\}$. As the applications of the above
unilateral global bifurcation result, we study the existence of nodal solutions
for a class of quasilinear elliptic problems with sign-changing weight.
Moreover, based on the bifurcation result of Dr\'{a}bek and Huang (1997)
[\ref{DH}], we study the existence of one-sign solutions for a class of high
dimensional quasilinear elliptic problems with sign-changing weight.

Analysis of PDEs