In the present paper, we establish a multiplicity result for a following class of nonlocal Neumann eigenvalue problem involving the fractional p-Laplacian. \(\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^{s}_{p}u + a(x) \left| u\right| ^{p-2}u =\lambda h(x,u) & \text{ in } \Omega , \\ \mathcal {N}_{s,p}u=0 & \text{ in } \mathbb {R}^N {\setminus } \overline{\Omega }. \end{array}\right. } \end{aligned}\) Precisely, we demonstrate the existence of an open interval for positive eigenvalues \(\lambda \) , for which the problem has at least three non-zero solutions in \(W^{s,p}_{\Omega }.\)
