### 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.

#### Article information

Source
Adv. Oper. Theory, Volume 4, Number 2 (2019), 539-555.

Dates
Accepted: 18 November 2018
First available in Project Euclid: 1 December 2018

https://projecteuclid.org/euclid.aot/1543633243

Digital Object Identifier
doi:10.15352/aot.1809-1420

Mathematical Reviews number (MathSciNet)
MR3883152

Subjects
Primary: 35R11: Fractional partial differential equations
Secondary: 35P30‎ ‎35J20

#### Citation

‎Azroul‎, E.; ‎Benkirane‎, A.; ‎Shimi‎, M. Eigenvalue problems involving the fractional $p(x)$-Laplacian operator. Adv. Oper. Theory 4 (2019), no. 2, 539--555. doi:10.15352/aot.1809-1420. https://projecteuclid.org/euclid.aot/1543633243

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