In this article, we provide existence results to the following nonlocal equation (Formula presented) where (Formula presented) is the fractional p-Laplacian operator. Here Ω ⊂ RN is a smooth bounded domain, s ∈ (0, 1), p > 1 and N > sp. We establish existence of at least one weak solution for (Pλ) when g(x, u) = f(x)u−q(x) and existence of at least two weak solutions when g(x, u) = λu−q(x) + ur for a suitable range of λ > 0. Here (Formula presented) where (Formula presented) is the critical Sobolev exponent and (Formula presented). © 2020 American Institute of Mathematical Sciences. All rights reserved.