{"paper":{"title":"Nonlinear Schr\\\"odinger equations with a critical, inverse-square potential","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Konysz, Bartosz Bieganowski, Simone Secchi","submitted_at":"2026-02-18T15:11:37Z","abstract_excerpt":"We study the existence of solutions of the following nonlinear Schr\\\"odinger equation $$ -\\Delta u+V(x)u-\\frac{(N-2)^2}{4|x|^2}u=f(x,u) $$ where $V:\\mathbb{R}^N\\to\\mathbb{R}$ and $f:\\mathbb{R}^N\\times \\mathbb{R}\\to \\mathbb{R}$ are periodic with respect to $x\\in\\mathbb{R}^N.$ We assume that $V$ has positive essential infimum, $f$ satisfies weak growth conditions and $N\\geq 3$. The approach to the problem uses variational methods with nonstandard functional setting. We obtain the existence of the ground state solution using the new profile decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.16524","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/2602.16524/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"}