{"id":"https://openalex.org/W7225137994","doi":"https://doi.org/10.48550/arxiv.2611.02980","title":"Symmetry, uniqueness and nondegeneracy of positive solutions of the Choquard equation","display_name":"Symmetry, uniqueness and nondegeneracy of positive solutions of the Choquard equation","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225137994","doi":"https://doi.org/10.48550/arxiv.2611.02980"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.02980","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02980","pdf_url":"https://arxiv.org/pdf/2611.02980","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2611.02980","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160533828","display_name":"Song Fan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fan, Song","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160540667","display_name":"Gui-Dong Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Gui-Dong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5160407746","display_name":"Jianjun Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Jianjun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/choquard-equation","display_name":"Choquard equation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/positive-solutions","display_name":"positive solutions","score":0.9509999752044678},{"id":"https://openalex.org/keywords/symmetry-of-solutions","display_name":"symmetry of solutions","score":0.7710000276565552},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.9010000228881836},{"id":"https://openalex.org/keywords/nondegeneracy","display_name":"nondegeneracy","score":0.9200000166893005},{"id":"https://openalex.org/keywords/riesz-potential","display_name":"Riesz potential","score":0.9639999866485596},{"id":"https://openalex.org/keywords/critical-sobolev-exponent","display_name":"critical Sobolev exponent","score":0.7699999809265137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.654699981212616},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6220999956130981},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5199000239372253},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5059999823570251},{"id":"https://openalex.org/C189987565","wikidata":"https://www.wikidata.org/wiki/Q7333166","display_name":"Riesz potential","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3779999911785126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37130001187324524},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2651999890804291},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.24770000576972961}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.02980","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02980","pdf_url":"https://arxiv.org/pdf/2611.02980","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2611.02980","doi":"https://doi.org/10.48550/arxiv.2611.02980","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.02980","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2611.02980","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02980","pdf_url":"https://arxiv.org/pdf/2611.02980","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4226331147","https://openalex.org/W2933543993","https://openalex.org/W2620897076","https://openalex.org/W2883376202","https://openalex.org/W4396916254","https://openalex.org/W2998866759","https://openalex.org/W4404627282","https://openalex.org/W4283726091","https://openalex.org/W2084081621","https://openalex.org/W7218784683"],"abstract_inverted_index":{"We":[0],"study":[1],"positive":[2],"solutions":[3],"\\(Q\\in":[4],"H^1(\\mathbb":[5],"R^N)\\)":[6],"of":[7,15],"\\[-\u0394Q+Q=(I_\u03b1*Q^p)Q^{p-1},\\]":[8],"where":[9],"\\(I_\u03b1\\)":[10],"is":[11],"the":[12],"Riesz":[13],"potential":[14],"order":[16],"\\(\u03b1\\),":[17],"\\(N\\ge1\\),":[18],"\\(0<\u03b11+\u03b1/N\\),":[19],"and":[20],"\\((N-2)p":[21]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}
