On the nonlinear eigenvalue problems involving the fractional p-Laplacian operator with singular weight

The aim of this paper is to study the following problem with the p-Laplacian fractional involving singular weightswhere Ω is a bounded domain of R N (N ≥ 3) with smooth boundary ∂ Ω.The existence and the properties of the principal eigenvalue, such as simplicity, isolation, and corresponding eigenfunctions are obtained.Finally, we study the nonexistence of solutions by using a type version of Picone's identity.