Multiplicity results for stationary Kirchhoff problems involving fractional elliptic operator and critical nonlinearity in RN

Abstract

In this paper, we study a class of stationary Kirchhoff problems involving a fractional elliptic operator and critical nonlinearity in RN: g[u]s2(−Δ)su=αk(x)|u|q−2u+β|u|2s*−2u. By using a fractional version of Lions’ second concentration compactness principle and concentration compactness principle at infinity to prove that the (PS)c condition holds locally and by minimax methods and Krasnoselskii genus theory, we establish the multiplicity of solutions for suitable positive parameters α, β.