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The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations $$\n  -\\Delta u + u = \\big(I_\\alpha \\ast |u|^p\\big)|u|^{p-2}u \\quad\\text{in }\\; \\mathbb R^N$$ when $p\\searrow 2$. The existence of minimal action nodal solutions for $p>2$ can be proved using a variational minimax procedure over 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":"1511.04779","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-15T23:15:57Z","cross_cats_sorted":[],"title_canon_sha256":"721e4472460f8ff9342632e42e02ea2d853eb27e8f742570d4cebf2eb28c3e82","abstract_canon_sha256":"4972c4542ee634ea61d0d4dd794bdf957552a84c57cffec18231ad33e18ed4d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:08.352188Z","signature_b64":"ahfz6iosOc8fwKAawjkIiQqeLfvIKzshaXI5fjfKPNjKBNjzAfNB3n29kEZklKxA8BTo5JXZzGWtGi4ah9VfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7b2f02a92c5b448bd2ff2637826a012080a4745da39a2a9fdcd92ecb6cba986","last_reissued_at":"2026-05-18T00:41:08.351632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:08.351632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Least action nodal solutions for the quadratic Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen, Marco Ghimenti, Vitaly Moroz","submitted_at":"2015-11-15T23:15:57Z","abstract_excerpt":"We prove the existence of a minimal action nodal solution for the quadratic Choquard equation $$ -\\Delta u + u = \\big(I_\\alpha \\ast |u|^2\\big)u \\quad\\text{in }\\; \\mathbb R^N,$$ where $I_\\alpha$ is the Riesz potential of order $\\alpha\\in(0,N)$. The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations $$\n  -\\Delta u + u = \\big(I_\\alpha \\ast |u|^p\\big)|u|^{p-2}u \\quad\\text{in }\\; \\mathbb R^N$$ when $p\\searrow 2$. 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