Eigenvalue problems involving the fractional $p(x)$-Laplacian operator

Abstract

‎ ‎‎In this paper‎, ‎we study a nonlocal eigenvalue problem involving variable exponent growth conditions‎, ‎on a bounded domain $\Omega \subset \mathbb{R}^n$‎. ‎Using adequate variational techniques‎, ‎mainly based on Ekeland's variational principle‎, ‎we establish the existence of a continuous family of eigenvalues lying in a neighborhood at the right of the origin‎.