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Alves, Minbo Yang","submitted_at":"2015-10-06T01:33:08Z","abstract_excerpt":"We study the existence of multi-bump solutions to Choquard equation $$ \\begin{array}{ll} -\\Delta u + (\\lambda a(x)+1)u=\\displaystyle\\big(\\frac{1}{|x|^{\\mu}}\\ast |u|^p\\big)|u|^{p-2}u \\mbox{ in } \\,\\,\\, \\R^3, \\end{array} $$ where $\\mu \\in (0,3), p\\in(2, 6-\\mu)$, $\\lambda$ is a positive parameter and the nonnegative function $a(x)$ has a potential well $ \\Omega:=int (a^{-1}(0))$ consisting of $k$ disjoint bounded components $ \\Omega:=\\cup_{j=1}^{k}\\Omega_j$. We prove that if the parameter $\\lambda$ is large enough then the equation has at least $2^{k}-1$ multi-bump solutions."},"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":"1510.01409","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-06T01:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"a6410f9b6517e775e7e525d9dd17a758a97d5293652a2be319bb7f5648d0ced4","abstract_canon_sha256":"39bc5cf3e48510c4731bfe944d69b7feeb03c818ce6dced3b4278f36a325ddc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:37.575059Z","signature_b64":"+2IqC5aRcbwfFLPLoQmSVEs82eAXRb7Ak1cX/jkVcPu3UZNYDn2uH182yS9FZtiDCjAm3EKRDxDbtHH8ZzzbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8efa865bd157deaf138ff6d021273c9c65b37b868810a463e99ba62d8566fe65","last_reissued_at":"2026-05-18T01:16:37.574501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:37.574501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-bump solutions for Choquard equation with deepening potential well","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Al\\^annio B. N\\'obrega, Claudianor O. Alves, Minbo Yang","submitted_at":"2015-10-06T01:33:08Z","abstract_excerpt":"We study the existence of multi-bump solutions to Choquard equation $$ \\begin{array}{ll} -\\Delta u + (\\lambda a(x)+1)u=\\displaystyle\\big(\\frac{1}{|x|^{\\mu}}\\ast |u|^p\\big)|u|^{p-2}u \\mbox{ in } \\,\\,\\, \\R^3, \\end{array} $$ where $\\mu \\in (0,3), p\\in(2, 6-\\mu)$, $\\lambda$ is a positive parameter and the nonnegative function $a(x)$ has a potential well $ \\Omega:=int (a^{-1}(0))$ consisting of $k$ disjoint bounded components $ \\Omega:=\\cup_{j=1}^{k}\\Omega_j$. 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