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More precisely, we consider for $0<s<1$ the equation $$ (-\\Delta)^s u + V(x)u=Q(x)|u|^{p-2}u \\quad\\text{in }\\mathbb{R}^N,\\ N\\geq 1,$$ where the exponent $p$ is superlinear but subcritical, and $V>0$, $Q\\geq 0$ are bounded functions converging to $1$ as $|x|\\to\\infty$. Using a min-max procedure introduced by Bahri and Li we prove the existence of a positive solution under one-sided asymptotic bounds for $V$ and $Q$."},"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":"1312.7068","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-26T08:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"418b8b9ba923b3819247b421c6ca9f02737f408133ff01ffdc050f3c61e8b9a9","abstract_canon_sha256":"7a207bcf1539c5ba1b437f609872cc777f3ce7fa70302455183d022cf21d9ca8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:31.736805Z","signature_b64":"uHBEJPQr1anjlUc2VmWPQHZQbXooU9DP2dALdv1AWNgZSploBkaXgjHTfUuH2Dl1wE5GQ4xL40xP7qIWEqH5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d50fc9bdf0e1aa77437a195fb033c266c2410a07ed0740ec36c6582c6d8c240","last_reissued_at":"2026-05-18T02:45:31.736206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:31.736206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive solutions to some nonlinear fractional Schr\\\"odinger equations via a min-max procedure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gilles Ev\\'equoz, Mouhamed Moustapha Fall","submitted_at":"2013-12-26T08:51:21Z","abstract_excerpt":"The existence of a positive solution to the following fractional semilinear equation is proven, in a situation where a ground state solution may not exist. 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