{"paper":{"title":"Ground states for strongly indefinite Schr\\\"{o}dinger equations with competing nonlinearities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bartosz Bieganowski","submitted_at":"2026-06-23T18:53:51Z","abstract_excerpt":"We survey recent variational methods for strongly indefinite Schr\\\"{o}dinger equations with sign-changing nonlinearities. The main object is an energy functional of the form \\[ J(u)=\\frac12\\|u^+\\|^2-\\frac12\\|u^-\\|^2 -\\int_{\\mathbb{R}^N}F(u)\\,dx+\\lambda\\int_{\\mathbb{R}^N}G(u)\\,dx, \\] where the splitting $X=X^+\\oplus X^-$ is induced by a spectral gap of the linear Schr\\\"{o}dinger operator, and where the nonlinear part \\[ I(u)=\\int_{\\mathbb{R}^N}F(u)\\,dx-\\lambda\\int_{\\mathbb{R}^N}G(u)\\,dx \\] is allowed to change sign. We discuss the generalized linking theorem developed for such functionals, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25090","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/2606.25090/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"}