Bifurcation and multiplicity results for critical problems involving the p -Grushin operator

In this article, we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator Δ γp. We extend to a generic p > 1 a result, which was proved only when p=2. When p ≠ 2, the nonlinear operator - Δ γp has no linear eigenspaces, so our extension is nontrivial and requires an abstract critical theorem, which is not based on linear subspaces. We use an abstract result based on a pseudo-index related to the ℤ2 -cohomological index that is applicable here. We provide a version of the Lions' concentration-compactness principle for our operator.