In this article, we study the existence of weak solutions for a fractional type problem driven by a nonlocal operator of elliptic type (-Δ)sa1u - λa2(|u|)u = ƒ(x, u) + g(x)|u|q(x)-2u in Ω u = 0 in ℝN \ Ω. Our approach is based on critical point theorems and variational methods.