$p$-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.

arXiv admin note: text overlap with arXiv:1602.01071, arXiv:1407.4505, arXiv:1406.6242

Cited by in corpus (1)

• The Brezis-Nirenberg problem for the fractional $p$-Laplacian involving critical Hardy-Sobolev exponents