$$\varvec{p}$$-Laplacian problems involving critical Hardy–Sobolev exponents

Abstract

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.