Three non-zero solutions of a Neumann eigenvalue problems involving the fractional p-Laplacian

Abstract

In the present paper, we establish a multiplicity result for a following class of nonlocal Neumann eigenvalue problems involving the fractional p-Laplacian. \begin{align} \begin{cases} (-Δ)^{s}_{p}u + a(x) \abs{u}^{p-2}u =λh(x,u) & \text {in } Ω, \mathcal{N}_{s,p}u=0 & \text {in } \mathbb{R}^N \setminus \overlineΩ, \end{cases} \end{align} 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 $W_{\Omega }^{s,p}.$

11 pages