Existence of solution for a nonlocal elliptic problem with a Robin-type data

The aim of this work is to study the elliptic problem: (−Δp)su+|u|p−2u=μf(x,u)+λu−γ in Ω,u>0 in Ω,Npsu+α(x)|u|p−2u=0 in RN∖Ω, under some conditions on the nonlinearity f. Here 2≤p≤ps∗, μ,λ>0, 0<s,γ<1, α∈L∞(RN∖Ω). We will prove the existence of at least one solution using the variational principle and the Mountain pass theorem.