{"paper":{"title":"Liouville-type theorems for sign-changing solutions to nonlocal elliptic inequalities and systems with variable-exponent nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ahmad Z. 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. Next, we extend our stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.12167","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.12167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}