  We study the nonlinear one-dimensional $p$-Laplacian equation $$
-(y'^{(p-1)})'+(p-1)q(x)y^{(p-1)}=(p-1)w(x)f(y) on (0,1),$$ with linear
separated boundary conditions. We give sufficient conditions for the existence
of solutions with prescribed nodal properties concerning the behavior of
$f(s)/s^{(p-1)}$ when $s$ are at infinity and zero. These results are more
general and complementary for previous known ones for the case $p=2$ and $q$ is
nonnegative.
