Abstract
In this paper, we study the existence of positive solution for the following class of fractional elliptic equation ϵ2s(−Δ)su+V(z)u=λuq−2u+u2s∗−2uinRN, where ϵ, λ > 0 are positive parameters, q∈(2,2s∗),2s∗=2NN−2s,N>2s,s∈(0,1),(−Δ)su is the fractional Laplacian, and V is a saddle-like potential. The result is proved by using minimizing method constrained to the Nehari manifold. A special minimax level is obtained by using an argument made by Benci and Cerami.
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