{"id":"https://openalex.org/W4376614031","doi":"https://doi.org/10.1080/17476933.2023.2209727","title":"A Hopf type lemma for nonlocal pseudo-relativistic equations and its applications","display_name":"A Hopf type lemma for nonlocal pseudo-relativistic equations and its applications","publication_year":2023,"publication_date":"2023-05-15","ids":{"openalex":"https://openalex.org/W4376614031","doi":"https://doi.org/10.1080/17476933.2023.2209727"},"language":"en","primary_location":{"id":"doi:10.1080/17476933.2023.2209727","doi":"https://doi.org/10.1080/17476933.2023.2209727","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/17476933.2023.2209727","pdf_url":null,"source":{"id":"https://openalex.org/S77333429","display_name":"Complex Variables and Elliptic Equations","issn_l":"1747-6933","issn":["1747-6933","1747-6941"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex Variables and Elliptic Equations","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4376614031"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033783020","display_name":"Pengyan Wang","orcid":"https://orcid.org/0000-0002-2315-1771","observed_orcids":["https://orcid.org/0000-0002-2315-1771"]},"institutions":[{"id":"https://openalex.org/I130750295","display_name":"Xinyang Normal University","ror":"https://ror.org/0190x2a66","country_code":"CN","type":"education","lineage":["https://openalex.org/I130750295"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Pengyan Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Xinyang Normal University, Xinyang, Henan, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-2315-1771","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xinyang Normal University, Xinyang, Henan, People's Republic of China","institution_ids":["https://openalex.org/I130750295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033783020"],"corresponding_institution_ids":["https://openalex.org/I130750295"],"apc_list":null,"apc_paid":null,"fwci":0.2143,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.30010622,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"69","issue":"7","first_page":"1224","last_page":"1243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9984999895095825,"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":0.9984999895095825,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.00019999999494757503,"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/fractional-laplacian","display_name":"fractional Laplacian","score":0.9100000262260437},{"id":"https://openalex.org/keywords/moving-plane-method","display_name":"moving plane method","score":0.902999997138977},{"id":"https://openalex.org/keywords/radial-symmetry","display_name":"radial symmetry","score":0.9629999995231628}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6952434778213501},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.685497522354126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6563935279846191},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5858905911445618},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.47113341093063354},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4657227694988251},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44818922877311707},{"id":"https://openalex.org/C101682238","wikidata":"https://www.wikidata.org/wiki/Q868967","display_name":"Klein\u2013Gordon equation","level":3,"score":0.4272606670856476},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42543062567710876},{"id":"https://openalex.org/C168997771","wikidata":"https://www.wikidata.org/wiki/Q2022629","display_name":"Relativistic particle","level":3,"score":0.41028711199760437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3712543845176697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2532505691051483},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14382478594779968},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/17476933.2023.2209727","doi":"https://doi.org/10.1080/17476933.2023.2209727","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/17476933.2023.2209727","pdf_url":null,"source":{"id":"https://openalex.org/S77333429","display_name":"Complex Variables and Elliptic Equations","issn_l":"1747-6933","issn":["1747-6933","1747-6941"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex Variables and Elliptic Equations","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4317453918","display_name":null,"funder_award_id":"12101530","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335834","display_name":"Nanhu Scholars Program for Young Scholars of Xinyang Normal University","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1619948042","https://openalex.org/W1964819665","https://openalex.org/W1978730764","https://openalex.org/W2040019013","https://openalex.org/W2046904024","https://openalex.org/W2069914251","https://openalex.org/W2070347609","https://openalex.org/W2079503946","https://openalex.org/W2107784368","https://openalex.org/W2172034033","https://openalex.org/W2192231860","https://openalex.org/W2313278888","https://openalex.org/W2524438130","https://openalex.org/W2565981463","https://openalex.org/W2740444080","https://openalex.org/W2904164350","https://openalex.org/W2904988423","https://openalex.org/W2905296685","https://openalex.org/W2905369598","https://openalex.org/W2941929644","https://openalex.org/W2962757073","https://openalex.org/W2962882327","https://openalex.org/W2963300740","https://openalex.org/W2963348250","https://openalex.org/W2963686486","https://openalex.org/W2963806235","https://openalex.org/W2963855588","https://openalex.org/W2964240101","https://openalex.org/W2980321911","https://openalex.org/W2993817511","https://openalex.org/W3045960104","https://openalex.org/W3047784567","https://openalex.org/W3096009767","https://openalex.org/W3129631139","https://openalex.org/W3132436105","https://openalex.org/W3162569204","https://openalex.org/W3169118448","https://openalex.org/W3188762861","https://openalex.org/W3196366056","https://openalex.org/W3205646040","https://openalex.org/W3217362339","https://openalex.org/W4285105094"],"related_works":["https://openalex.org/W7127317971","https://openalex.org/W4399264599","https://openalex.org/W4214928902","https://openalex.org/W7147161429","https://openalex.org/W3169118448","https://openalex.org/W2895867527","https://openalex.org/W2962757073","https://openalex.org/W4214906194","https://openalex.org/W2254343690","https://openalex.org/W2029100775"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,92,114],"consider":[4],"the":[5,9,24,31,41,73,106,111,116,125,132,138,149],"nonlinear":[6,127],"equation":[7,130],"involving":[8],"nonlocal":[10,20,32,64,88,98,128,155],"pseudo-relativistic":[11,21,25,33,65,89,99,129,156],"operators":[12,49],"(\u2212\u0394+m2)su(x)=f(x,u(x)),":[13],"where":[14],"0<s<1":[15],"and":[16,110,119],"mass":[17],"m>0.":[18],"The":[19,78],"operator":[22,27,34,44],"includes":[23],"Schr\u00f6dinger":[26],"\u2212\u0394+m2.":[28],"When":[29],"m\u21920+,":[30],"(\u2212\u0394+m2)s":[35],"is":[36,81],"also":[37],"closely":[38],"related":[39],"to":[40,63,82,87,97,124,158],"fractional":[42],"Laplacian":[43],"(\u2212\u0394)s.":[45],"But":[46],"these":[47],"two":[48],"are":[50],"quite":[51],"different.":[52],"We":[53,135],"first":[54],"establish":[55],"a":[56,69,84,94,144],"Hopf":[57,107,139],"type":[58,108,140],"lemma":[59,109,141],"for":[60],"anti-symmetric":[61],"functions":[62],"operators,":[66],"which":[67],"play":[68],"key":[70],"role":[71],"in":[72,131,147],"method":[74,150],"of":[75,121,151,162],"moving":[76,152],"planes.":[77],"main":[79],"difficulty":[80],"construct":[83],"suitable":[85],"sub-solution":[86],"operators.":[90,100],"Then":[91],"prove":[93],"pointwise":[95,112],"estimate":[96],"As":[101],"an":[102],"application,":[103],"combined":[104],"with":[105],"estimate,":[113],"obtain":[115,159],"radial":[117],"symmetry":[118],"monotonicity":[120],"positive":[122],"solutions":[123],"above":[126],"whole":[133],"space.":[134],"believe":[136],"that":[137],"will":[142],"become":[143],"powerful":[145],"tool":[146],"applying":[148],"planes":[153],"on":[154],"equations":[157],"qualitative":[160],"properties":[161],"solutions.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2023-05-17T00:00:00"}
