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Assuming that \\begin{equation*} V(x)=V_\\infty+\\frac{a}{|x|^m}+O\\Big(\\frac{1}{|x|^{m+\\sigma}}\\Big),\\ \\text{as}\\ |x|\\rightarrow+\\infty, %\\tag{$V2$} \\end{equation*} for instance if $p>2$, $m>2$ and $\\sigma>1$ we prove the existence of infinitely many positive solutions. If $V(x)$ is radially symmetric, this result was proved in"},"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":"1309.7196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-27T10:26:51Z","cross_cats_sorted":[],"title_canon_sha256":"e135251ceef7a8bdedf9f3dedec9af8bc8ab1caaa18bf79f3245f9ac229242ba","abstract_canon_sha256":"90019bfa1fce2fb1128c2d00310c7558cc62a4b55cd3c8bea849c1d89cdd17ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:59.899411Z","signature_b64":"sbhXSFqTswljSVmYLmwiKtgPJJ9GGMncWnACluogLi8/emq592B/Gk5NnVxnR3noi90FL2uTF66yiccvsuauDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00c397a20982475ce3106289611584b4c4afc5f3605805c16f8cd73396cb5392","last_reissued_at":"2026-05-18T03:11:59.898803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:59.898803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many positive solutions of nonlinear Schr\\\"{o}dinger equations with non-symmetric potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Manuel del Pino, Wei Yao","submitted_at":"2013-09-27T10:26:51Z","abstract_excerpt":"We consider the standing-wave problem for a nonlinear Schr\\\"{o}dinger equation, corresponding to the semilinear elliptic problem \\begin{equation*} -\\Delta u+V(x)u=|u|^{p-1}u,\\ u\\in H^1(\\mathbb{R}^2), \\end{equation*} where $V(x)$ is a uniformly positive potential and $p>1$. Assuming that \\begin{equation*} V(x)=V_\\infty+\\frac{a}{|x|^m}+O\\Big(\\frac{1}{|x|^{m+\\sigma}}\\Big),\\ \\text{as}\\ |x|\\rightarrow+\\infty, %\\tag{$V2$} \\end{equation*} for instance if $p>2$, $m>2$ and $\\sigma>1$ we prove the existence of infinitely many positive solutions. 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