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First, the existence of a groundstate solutions using minimization method on the associated Nehari manifold is obtained. Next, the existence of least energy sign-changing solutions is investigated by considering the Nehari nodal set."},"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":"1705.05775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-16T15:49:48Z","cross_cats_sorted":[],"title_canon_sha256":"f5d150479d2ca7968f2bafb1f256e989c81c97b79647490314e0e7e035a79a9e","abstract_canon_sha256":"3577b547f5c324246762c96955b1eb220f1755f4e0616bfbd7b9469bfe85a1c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:20.205210Z","signature_b64":"Gh4wRUL0IQxIkeW/upEYJPWYkZa4CyMpUpxXtWYp1GQWib1ZAJo+qzv3VcGINbNnOFwkpqpt62ECeXV2E7NhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39fd6561df113ed7342945420b3bad3bd006706bf343c07a5b64bb2969bb9a4c","last_reissued_at":"2026-05-18T00:44:20.204788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:20.204788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlocal Pertubations of Fractional Choquard Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gurpreet Singh","submitted_at":"2017-05-16T15:49:48Z","abstract_excerpt":"We study the equation \\begin{equation} (-\\Delta)^{s}u+V(x)u= (I_{\\alpha}*|u|^{p})|u|^{p-2}u+\\lambda(I_{\\beta}*|u|^{q})|u|^{q-2}u \\quad\\mbox{ in } \\R^{N}, \\end{equation} where $I_\\gamma(x)=|x|^{-\\gamma}$ for any $\\gamma\\in (0,N)$, $p, q >0$, $\\alpha,\\beta\\in (0,N)$, $N\\geq 3$ and $ \\lambda \\in R$. First, the existence of a groundstate solutions using minimization method on the associated Nehari manifold is obtained. Next, the existence of least energy sign-changing solutions is investigated by considering the Nehari nodal set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05775","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.05775","created_at":"2026-05-18T00:44:20.204856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.05775v1","created_at":"2026-05-18T00:44:20.204856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05775","created_at":"2026-05-18T00:44:20.204856+00:00"},{"alias_kind":"pith_short_12","alias_value":"HH6WKYO7CE7N","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HH6WKYO7CE7NONBJ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HH6WKYO7","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.02536","citing_title":"The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\\R}^n$ with a Hardy term","ref_index":45,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP","json":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP.json","graph_json":"https://pith.science/api/pith-number/HH6WKYO7CE7NONBJIVBAWO5NHP/graph.json","events_json":"https://pith.science/api/pith-number/HH6WKYO7CE7NONBJIVBAWO5NHP/events.json","paper":"https://pith.science/paper/HH6WKYO7"},"agent_actions":{"view_html":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP","download_json":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP.json","view_paper":"https://pith.science/paper/HH6WKYO7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.05775&json=true","fetch_graph":"https://pith.science/api/pith-number/HH6WKYO7CE7NONBJIVBAWO5NHP/graph.json","fetch_events":"https://pith.science/api/pith-number/HH6WKYO7CE7NONBJIVBAWO5NHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP/action/storage_attestation","attest_author":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP/action/author_attestation","sign_citation":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP/action/citation_signature","submit_replication":"https://pith.science/pith/HH6WKYO7CE7NONBJIVBAWO5NHP/action/replication_record"}},"created_at":"2026-05-18T00:44:20.204856+00:00","updated_at":"2026-05-18T00:44:20.204856+00:00"}