Mathematics

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

E. Azroul, A. Benkirane, M. Shimi

2019.4.1Advances in Operator Theory

DOI: 10.15352/aot.1809-1420

tlooto Summary

The paper studies eigenvalue problems involving the fractional p(x)-Laplacian operator on a bounded domain Ω ⊂ R, establishing the existence of continuous families of eigenvalues using Ekeland's variational principle.

Abstract

In this paper, we study a nonlocal eigenvalue problem involving variable exponent growth conditions, on a bounded domain Ω ⊂ R. 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.

Citation format

AZROUL, E.; BENKIRANE, A.; SHIMI, M. Eigenvalue problems involving the fractional $p(x)$-laplacian operator. Advances in Operator Theory, 2019.