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Fino, Bessem Samet, Mohamed Jleli","submitted_at":"2020-03-26T22:02:17Z","abstract_excerpt":"We consider the fractional elliptic inequality with variable-exponent nonlinearity $$ (-\\Delta)^{\\frac{\\alpha}{2}} u+\\lambda\\, \\Delta u \\geq |u|^{p(x)}, \\quad x\\in\\mathbb{R}^N, $$ where $N\\geq 1$, $\\alpha\\in (0,2)$, $\\lambda\\in\\mathbb{R}$ is a constant, $p: \\mathbb{R}^N\\to (1,\\infty)$ is a measurable function, and $(-\\Delta)^{\\frac{\\alpha}{2}}$ is the fractional Laplacian operator of order $\\frac{\\alpha}{2}$. A Liouville-type theorem is established for the considered problem. Namely, we obtain sufficient conditions under which the only weak solution is the trivial one. 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