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In this paper we will prove the existence of three nontrivial weak solutionsof the following problem involving a nonlinear integro-differential operatorand a term with critical exponent. \begin{align*} \begin{split}-\mathscr{L}_\Phi u & = |u|^{{p_{s}^{\ast}}-2}u+\lambdaf(x,u)\,\,\mbox{in}\,\,\Omega,\\ u & = 0\,\, \mbox{in}\,\,\mathbb{R}^N\setminus \Omega, \end{split} \end{align*} Here $q\in(p, p_s^*)$,where $p_s^*$ is the fractional Sobolev conjugate of $p$ and $-\mathscr{L}_\Phi$ represents a general nonlocal integro-differential operator of order$s\in(0,1)$. This operator is possibly degenerate and covers the case offractional $p$-Laplacian operator.

Three nontrivial solutions of a nonlocal problem involving critical exponent