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We assume that $\\inf\\sigma(-\\Delta+V)>0$, where $\\sigma(-\\Delta+V)$ stands for the spectrum of $-\\Delta +V$ and $f$ has the subcritical growth but higher than $\\Gamma(x)|u|^{q-2}u$, ho"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.05078","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-16T16:20:17Z","cross_cats_sorted":[],"title_canon_sha256":"3c37725606281f633274c021487c938c7556965aa50ca38f80e9e5e742aa75c1","abstract_canon_sha256":"2d0931e6a1119555afc33a7325b5975432cfcdc55ff5cfdb7e5572731653fe75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:23.981255Z","signature_b64":"hGhptlrJ6RA96afgXdWCv3ZWS3L3Rv1PiE6rqmLl3FG63AXRWo5ypZfjSKrCOl4VhoI/NlA/mO73pWEL7P8qAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa7db0839a1472306367409a8275c292196a7c10b3ae8d6f7fa81d889c5aaeb2","last_reissued_at":"2026-05-18T00:07:23.980850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:23.980850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Schr\\\"odinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bartosz Bieganowski, Jaros{\\l}aw Mederski","submitted_at":"2016-02-16T16:20:17Z","abstract_excerpt":"We look for ground state solutions to the following nonlinear Schr\\\"{o}dinger equation $$-\\Delta u + V(x)u = f(x,u)-\\Gamma(x)|u|^{q-2}u\\hbox{ on }\\mathbb{R}^N,$$ where $V=V_{per}+V_{loc}\\in L^{\\infty}(\\mathbb{R}^N)$ is the sum of a periodic potential $V_{per}$ and a localized potential $V_{loc}$, $\\Gamma\\in L^{\\infty}(\\mathbb{R}^N)$ is periodic and $\\Gamma(x)\\geq 0$ for a.e. $x\\in\\mathbb{R}^N$ and $2\\leq q<2^*$. 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