Advances in Operator Theory

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

E. ‎Azroul‎, A. ‎Benkirane‎, and M. ‎Shimi‎

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‎ ‎‎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

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

Received: 14 September 2018
Accepted: 18 November 2018
First available in Project Euclid: 1 December 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

Ekeland's variational principle‎ ‎‎fractional $p(x)$-Laplacian operator ‎fractional Sobolev spaces with variable exponent ‎ ‎‎eigenvalues problem


‎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.

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