Abdellatif Aglzim, Houssam Baladi, Najib Tsouli
Abstract:
We study nonlocal elliptic problems driven by the fractional
\((p_1(x,y),p_2(x,y))\)-Laplacian operator under Dirichlet boundary conditions,
where \(p_1(\cdot,\cdot)\) and \(p_2(\cdot,\cdot)\) are continuous functions defined on
a bounded domain \(\Omega\subset\mathbb{R}^N\) (\(N\geq 2\)).
The model includes indefinite weight functions, which may change the sign within the
domain. By applying variational methods, we establish the existence of at least one
nontrivial weak solution.
Our results extend recent contributions in the literature on nonlocal problems with
variable exponent operators, and provide new insights into the interaction between
fractional order, and sign-changing weights.
Submitted February 12, 2026. Published June 8, 2026.
Math Subject Classifications: 35A15, 35J60, 35R11, 35P30.
Key Words: Indefinite weight; fractional \( (p_1(x),p_2(x))\)-Laplacian operator;
variable exponent; Ekeland's variational principle; variational method.
DOI: 10.58997/ejde.2026.40
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Abdellatif Aglzim Mohamed I University Mathematics Department Faculty of Sciences, Oujda, Morocco email: abdellatif.aglzim@ump.ac.ma |
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Houssam Baladi Mohamed I University Mathematics Department Faculty of Science, Oujda, Morocco email: houssam.baladi@ump.ac.ma |
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Najib Tsouli Mohamed I University Mathematics Department Faculty of Sciences, Oujda, Morocco email: n.tsouli@ump.ac.ma |
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