This paper deals with the existence of multiple solutions
for the following critical fractional $p$-Laplacian problem
\begin{equation*}
\left\{
\begin{array}{l}
\mathbf{(-}\Delta \mathbf{)}_{p}^{s}u(x)=\lambda \left\vert u\right\vert
^{p-2}u+f(x,u)+\mu g(x,u)\ \text{in }\Omega ,u>0, \\
\\
u=0\text{ on}\ \mathbb{R}^{n}\setminus \Omega ,%
\end{array}%
\right.
\end{equation*}%
where $p>1$, $s\in (0,1)$, $\Omega \subset \mathbb{R}^{n}(n>ps),$ be a bounded smooth domain, $\lambda $, $\mu $ are positive parameters and the functions $f,g:\overline{%
\Omega }\times \lbrack 0,\infty )\longrightarrow [0,\infty),$ are continuous and differentiable with respect to the second variable. Our main tools are based on variational methods combined with a classical concentration
compacteness method.
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