A strongly indefinite Choquard equation with critical exponent due to the Hardy–Littlewood–Sobolev inequality

Name: Work Video:
Duration: 3 min 30 s
Fashun Gao; Minbo Yang
{'id': 'https://openalex.org/W2606453253', 'doi': 'https://doi.org/10.1142/s0219199717500377', 'title': 'A strongly indefinite Choquard equation with critical exponent due to the Hardy–Littlewood–Sobolev inequality', 'display_name': 'A strongly indefinite Choquard equation with critical exponent due to the Hardy–Littlewood–Sobolev inequality', 'publication_year': 2017, 'publication_date': '2017-04-21', 'ids': {'openalex': 'https://openalex.org/W2606453253', 'doi': 'https://doi.org/10.1142/s0219199717500377', 'mag': '2606453253'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1142/s0219199717500377', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S51811661', 'display_name': 'Communications in Contemporary Mathematics', 'issn_l': '0219-1997', 'issn': ['0219-1997', '1793-6683'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319815', 'host_organization_name': 'World Scientific', 'host_organization_lineage': ['https://openalex.org/P4310319815'], 'host_organization_lineage_names': ['World Scientific'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/pdf/1702.05287', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5064129688', 'display_name': 'Fashun Gao', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I135237710', 'display_name': 'Zhejiang Normal University', 'ror': 'https://ror.org/01vevwk45', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I135237710']}], 'countries': ['CN'], 'is_corresponding': False, 'raw_author_name': 'Fashun Gao', 'raw_affiliation_strings': ['Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China', 'institution_ids': ['https://openalex.org/I135237710']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5046001568', 'display_name': 'Minbo Yang', 'orcid': 'https://orcid.org/0000-0001-5676-6273'}, 'institutions': [{'id': 'https://openalex.org/I135237710', 'display_name': 'Zhejiang Normal University', 'ror': 'https://ror.org/01vevwk45', 'country_code': 'CN', 'type': 'education', 'lineage': ['https://openalex.org/I135237710']}], 'countries': ['CN'], 'is_corresponding': True, 'raw_author_name': 'Minbo Yang', 'raw_affiliation_strings': ['Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China', 'institution_ids': ['https://openalex.org/I135237710']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5046001568'], 'corresponding_institution_ids': ['https://openalex.org/I135237710'], 'apc_list': None, 'apc_paid': None, 'fwci': 8.879, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 54, 'citation_normalized_percentile': {'value': 0.999884, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 96, 'max': 97}, 'biblio': {'volume': '20', 'issue': '04', 'first_page': '1750037', 'last_page': '1750037'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10194', 'display_name': 'Nonlinear Partial Differential Equations', 'score': 0.9994, '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': 0.9994, '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': 0.9986, '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': 0.9903, '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/sobolev-inequality', 'display_name': 'Sobolev inequality', 'score': 0.48407093}, {'id': 'https://openalex.org/keywords/exponent', 'display_name': 'Exponent', 'score': 0.48380655}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.9354981}, {'id': 'https://openalex.org/C99730327', 'wikidata': 'https://www.wikidata.org/wiki/Q1501536', 'display_name': 'Sobolev space', 'level': 2, 'score': 0.7101572}, {'id': 'https://openalex.org/C185644265', 'wikidata': 'https://www.wikidata.org/wiki/Q3711848', 'display_name': 'Sobolev inequality', 'level': 3, 'score': 0.48407093}, {'id': 'https://openalex.org/C2780388253', 'wikidata': 'https://www.wikidata.org/wiki/Q5421508', 'display_name': 'Exponent', 'level': 2, 'score': 0.48380655}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.4615007}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.44502425}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C41895202', 'wikidata': 'https://www.wikidata.org/wiki/Q8162', 'display_name': 'Linguistics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1142/s0219199717500377', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S51811661', 'display_name': 'Communications in Contemporary Mathematics', 'issn_l': '0219-1997', 'issn': ['0219-1997', '1793-6683'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319815', 'host_organization_name': 'World Scientific', 'host_organization_lineage': ['https://openalex.org/P4310319815'], 'host_organization_lineage_names': ['World Scientific'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1702.05287', 'pdf_url': 'https://arxiv.org/pdf/1702.05287', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1702.05287', 'pdf_url': 'https://arxiv.org/pdf/1702.05287', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 37, 'referenced_works': ['https://openalex.org/W1510057272', 'https://openalex.org/W1536072638', 'https://openalex.org/W1566246025', 'https://openalex.org/W1659004305', 'https://openalex.org/W1960733295', 'https://openalex.org/W1988167079', 'https://openalex.org/W2001667545', 'https://openalex.org/W2009071934', 'https://openalex.org/W2011829237', 'https://openalex.org/W2011931926', 'https://openalex.org/W2013535418', 'https://openalex.org/W2018640789', 'https://openalex.org/W2019829221', 'https://openalex.org/W2032085094', 'https://openalex.org/W2035173346', 'https://openalex.org/W2038928461', 'https://openalex.org/W2040320111', 'https://openalex.org/W2052729963', 'https://openalex.org/W2054702340', 'https://openalex.org/W2079084750', 'https://openalex.org/W2082569036', 'https://openalex.org/W2087613667', 'https://openalex.org/W2114287606', 'https://openalex.org/W2115353264', 'https://openalex.org/W2142174898', 'https://openalex.org/W2269296822', 'https://openalex.org/W2275286668', 'https://openalex.org/W2338390751', 'https://openalex.org/W2962788244', 'https://openalex.org/W2963353752', 'https://openalex.org/W2963952991', 'https://openalex.org/W3098015761', 'https://openalex.org/W3099848444', 'https://openalex.org/W3104068651', 'https://openalex.org/W4231045816', 'https://openalex.org/W423201015', 'https://openalex.org/W4232306901'], 'related_works': ['https://openalex.org/W4390480869', 'https://openalex.org/W4389115881', 'https://openalex.org/W4319988904', 'https://openalex.org/W4319452538', 'https://openalex.org/W4287815684', 'https://openalex.org/W3193384681', 'https://openalex.org/W3135872487', 'https://openalex.org/W3015352488', 'https://openalex.org/W266838890', 'https://openalex.org/W2378397219'], 'abstract_inverted_index': {'In': [0], 'this': [1], 'paper,': [2], 'we': [3, 54], 'are': [4], 'concerned': [5], 'with': [6, 83], 'the': [7, 35, 51, 56, 71], 'following': [8], 'nonlinear': [9, 131], 'Choquard': [10, 132], 'equation': [11, 82], '[Formula:': [12, 16, 19, 23, 27, 38, 42], 'see': [13, 17, 20, 24, 28, 39, 43], 'text]': [14, 21, 29, 40, 44], 'where': [15], 'text],': [18], 'and': [22, 41, 69, 96, 120], 'text].': [25], 'If': [26], 'lies': [30], 'in': [31, 75], 'a': [32, 79, 102, 106, 128], 'gap': [33], 'of': [34, 37, 46, 58, 101, 125, 130], 'spectrum': [36], 'is': [45], 'critical': [47], 'growth': [48], 'due': [49], 'to': [50, 105], 'Hardy–Littlewood–Sobolev': [52], 'inequality,': [53], 'obtain': [55], 'existence': [57], 'nontrivial': [59, 103], 'solutions': [60], 'by': [61], 'variational': [62], 'methods.': [63], 'The': [64], 'main': [65], 'result': [66], 'here': [67], 'extends': [68], 'complements': [70], 'earlier': [72], 'theorems': [73], 'obtained': [74], '[N.': [76], 'Ackermann,': [77], 'On': [78], 'periodic': [80], 'Schrödinger': [81], 'nonlocal': [84], 'superlinear': [85], 'part,': [86], 'Math.': [87, 113, 136], 'Z.': [88], '248': [89], '(2004)': [90], '423–443;': [91], 'B.': [92], 'Buffoni,': [93], 'L.': [94], 'Jeanjean': [95], 'C.': [97], 'A.': [98], 'Stuart,': [99], 'Existence': [100, 124], 'solution': [104], 'strongly': [107], 'indefinite': [108], 'semilinear': [109], 'equation,': [110], 'Proc.': [111], 'Amer.': [112, 135], 'Soc.': [114, 137], '119': [115], '(1993)': [116], '179–186;': [117], 'V.': [118], 'Moroz': [119], 'J.': [121], 'Van': [122], 'Schaftingen,': [123], 'groundstates': [126], 'for': [127], 'class': [129], 'equations,': [133], 'Trans.': [134], '367': [138], '(2015)': [139], '6557–6579].': [140]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2606453253', 'counts_by_year': [{'year': 2024, 'cited_by_count': 4}, {'year': 2023, 'cited_by_count': 4}, {'year': 2022, 'cited_by_count': 10}, {'year': 2021, 'cited_by_count': 6}, {'year': 2020, 'cited_by_count': 11}, {'year': 2019, 'cited_by_count': 12}, {'year': 2018, 'cited_by_count': 6}, {'year': 2017, 'cited_by_count': 1}], 'updated_date': '2024-12-07T19:55:43.379984', 'created_date': '2017-04-28'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
