{"paper":{"title":"On a class of logarithmic Schr\\\"odinger equations via perturbation method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chen Huang, Zhipeng Yang","submitted_at":"2026-01-19T05:23:56Z","abstract_excerpt":"In this paper, we consider the following logarithmic Schr\\\"odinger equation\n  \\[\n  -\\Delta u + V(x)u = u \\log u^{2},\\quad x\\in\\mathbb{R}^{N}.\n  \\] Assuming that \\(V\\in C(\\mathbb{R}^{N},\\mathbb R)\\), \\(V\\) is bounded away from zero, and \\(V(x)\\to+\\infty\\) as \\(|x|\\to\\infty\\), we develop a new perturbative variational approach to overcome the lack of \\(C^{1}\\)-smoothness of the associated functional and prove the existence and multiplicity of nontrivial weak solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.12732","kind":"arxiv","version":2},"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/2601.12732/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"}