{"paper":{"title":"On the asymptotically linear problem for an elliptic equation with an indefinite nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Salda\\~na, Cristian Morales-Encinos, Mayra Soares, M\\'onica Clapp","submitted_at":"2025-11-07T19:45:22Z","abstract_excerpt":"We study the semilinear elliptic problem \\[ -\\Delta u = Q_{\\Omega} |u|^{p-2}u \\quad \\text{in } \\mathbb{R}^N, \\] where \\( Q_{\\Omega} = \\chi_{\\Omega} - \\chi_{\\mathbb{R}^N \\setminus \\Omega} \\) for a bounded smooth domain \\( \\Omega \\subset \\mathbb{R}^N \\), \\( N \\ge 3 \\), and \\( 1 < p < 2^{*} \\). This equation arises in the study of optical waveguides and exhibits indefinite nonlinearity due to the sign-changing weight \\( Q_{\\Omega} \\). We prove that, for \\( p > 2 \\) sufficiently close to \\( 2 \\), the problem admits a unique positive solution, which is nondegenerate. Our approach combines a detaile"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.05679","kind":"arxiv","version":3},"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/2511.05679/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"}