Multiplicity results for nonlocal fractional p-Kirchhoff equations via Morse theory

In this paper, we apply Morse theory and local linking to study the existence of nontrivial solutions for Kirchhoff type equations involving the nonlocal fractional p-Laplacian with homogeneous Dirichlet boundary conditions: {align*} {cases} \![M(_{R2N}\!{|u(x)-u(y)|^p}{|x-y|N+ps}dxdy)]ᵖ⁻¹ \!(-Δ)_p^su(x)=f(x,u)&in Ω,\\ u=0&in RNΩ, {cases} {align*} where Ω is a smooth bounded domain of RN, (-Δ)ₚˢ is the fractional p-Laplace operator with 0< s< 1< p< ∞ with $sp< N$, M R⁺₀→ R⁺ is a continuous and positive function not necessarily satisfying the increasing condition and f is a Carathéodory function satisfying some extra assumptions.