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Using minimax arguments, we obtain a positive ground state solution under general conditions on $f$ which we believe to be almost optimal."},"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":"1706.07149","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-22T02:22:03Z","cross_cats_sorted":[],"title_canon_sha256":"45775871034568240f10235d2a97c4799abe2e67115c9bb506229491a60db23a","abstract_canon_sha256":"7b421fb60235cf460a513b938e44aec3f57e67b024889d680a37963908ce95c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:49.268489Z","signature_b64":"0wkuPep2yydw/g+wKdDqa+AcM+4uutNNdjzG61ic3EQrWDrP2uU/zKUCWg230trsvz7Xaz1JI1YA58tNpG84Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdac7d5d66fe55ddc30f1c1a021a1579242947899f690e5280de72c709ad986e","last_reissued_at":"2026-05-18T00:36:49.268031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:49.268031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground state solution of fractional Schr\\\"odinger equations with a general nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yi He","submitted_at":"2017-06-22T02:22:03Z","abstract_excerpt":"In this paper, we study the following fractional Schr\\\"odinger equation: \\[ \\left\\{\\begin{gathered}\n  {(- \\Delta)^s}u + mu = f(u){\\text{in}}{\\mathbb{R}^N}, \\hfill\n  u \\in {H^s}({\\mathbb{R}^N}),{\\text{}}u > 0{\\text{on}}{\\mathbb{R}^N}, \\hfill \\\\ \\end{gathered} \\right. \\] where $m>0$, $N>2s$, ${(- \\Delta)^s}$, $s \\in (0,1)$ is the fractional Laplacian. 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