Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operator: $$(- Δ)ₚˢ u = λ u ᵖ⁻² u + ( ∫Ω{ u ^{pμ,s*}}{ x-y μ}\,dy ) u ^{pμ,s*-2}u in Ω, u = 0 in {R}N Ω, $$ where Ω is a bounded domain in ${R}N$ with Lipschitz boundary, λ is a real parameter, $p∈(1,∞)$ , $s∈ (0,1)$ , $N>sp$ , and $pμ,s*={(N-μ/2)p}{N-sp}$ is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. These extend results in the literature for the fractional Choquard problems, and they are still new for a p-Laplacian case.