#### H. Harcha, O. Chakrone, N. Tsouli, On the nonlinear eigenvalue problems involving the fractional p-Laplacian operator with singular weight, Vol. 2022 (2022), Article ID 40, pp. 1-14

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DOI: 10.23952/jnfa.2022.40

Received April 12, 2022; Accepted September 14, 2022; Published October 26, 2022

Abstract The aim of this paper is to study the following problem with the p-Laplacian fractional involving singular weights
$-(\Delta_{a})_{p}^{s} u + h_{b}(x) |u|^{p-2} u= \lambda h_{c}(x) |u|^{p-2} u + h(x)$ in $\Omega$,
$u=0$ on $\mathbb{R^{N}}\backslash\Omega,$
where $\Omega$ is a bounded domain of $\mathbb{R}^{N}$ $(N\geq 3)$ with smooth boundary $\partial\Omega$. 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.