Degenerate Kirchhoff-type diffusion problems involving the fractional p-Laplacian

In this paper we study the existence of a global solution for a diffusion problem of Kirchhoff type driven by a nonlocal integro-differential operator. As a particular case, we consider the following parabolic equation involving the fractional p-Laplacian: {∂tu+[u]s,p(λ−1)p(−Δ)psu=|u|q−2u,in  Ω×R+,∂tu=∂u/∂t,u(x,0)=u0(x),in  Ω,u(x,t)=0,in  (RN∖Ω)×R0+, where [u]s,p is the Gagliardo p-seminorm of u, Ω⊂RN is a bounded domain with Lipschitz boundary ∂Ω, p