Existence and Multiplicity of Solutions for Fractional $p$-Laplacian Equation Involving Critical Concave-convex Nonlinearities

Weimin Zhang

We investigate the following fractional $p$-Laplacian equation \[ \begin{cases} \begin{aligned} (-Δ)_p^s u&=λ|u|^{q-2}u+|u|^{p_s^*-2}u &&\text{in}~Ω,\\ u &=0 &&\text{in}~ \mathbb{R…