  We prove existence, multiplicity, and bifurcation results for $p$-Laplacian
problems involving critical Hardy-Sobolev exponents. Our results are mainly for
the case $\lambda \ge \lambda_1$ and extend results in the literature for $0 <
\lambda < \lambda_1$. In the absence of a direct sum decomposition, we use
critical point theorems based on a cohomological index and a related
pseudo-index.
