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We assume that $0$ does not lie in the spectrum of $-\\Delta+V$ and $\\mu<\\frac{(N-2)^2}{4}$, $N\\geq 3$. The superlinear and subcritical term $f$ satisfies a weak monotonicity condition. For sufficiently small $\\mu\\geq 0$ we find a ground state solution as "},"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":"1412.6022","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-18T19:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"4b604479ff4263952559499ab9320b759619e9a4e9132933f4b461e01bce56ac","abstract_canon_sha256":"8a12f40bfb97df5464a7c3afaee9d1a22f7ddc4d076ea680a6b015a6c7db1948"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:19.774234Z","signature_b64":"QJnJgozkPCE0Up+FleDl7Q1/TrYdyFpGEGgwo215a4uAaQow8SOH8F+JHZeyps/UyvWXxxoIOHcGt0XZFg6CBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca96e46597d2194d89623b7f51d037e917e9520d39fd943bc78f500b83824b05","last_reissued_at":"2026-05-18T01:21:19.773762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:19.773762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground states of nonlinear Schr\\\"odinger equations with sum of periodic and inverse-square potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaros{\\l}aw Mederski, Qianqiao Guo","submitted_at":"2014-12-18T19:30:06Z","abstract_excerpt":"We study the existence of solutions of the following nonlinear Schr\\\"odinger equation \\begin{equation*}\n  -\\Delta u + \\Big(V(x)-\\frac{\\mu}{|x|^2}\\Big) u = f(x,u)\n  \\hbox{ for } x\\in\\mathbb{R}^N\\setminus\\{0\\}, \\end{equation*} where $V:\\mathbb{R}^N\\to\\mathbb{R}$ and $f:\\mathrm{R}^N\\times\\mathbb{R}\\to\\mathbb{R}$ are periodic in $x\\in\\mathbb{R}$. We assume that $0$ does not lie in the spectrum of $-\\Delta+V$ and $\\mu<\\frac{(N-2)^2}{4}$, $N\\geq 3$. The superlinear and subcritical term $f$ satisfies a weak monotonicity condition. 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