{"id":"https://openalex.org/W2763330744","doi":"https://doi.org/10.1137/16m1107358","title":"Dynamic Bifurcation from Infinity of Nonlinear Evolution Equations","display_name":"Dynamic Bifurcation from Infinity of Nonlinear Evolution Equations","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2763330744","doi":"https://doi.org/10.1137/16m1107358","mag":"2763330744"},"language":"en","primary_location":{"id":"doi:10.1137/16m1107358","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1107358","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","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/A5063717168","display_name":"Chunqiu Li","orcid":"https://orcid.org/0000-0002-5270-8364"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chunqiu Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100770502","display_name":"Desheng Li","orcid":"https://orcid.org/0009-0007-4200-077X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Desheng Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100388936","display_name":"Zhijun Zhang","orcid":"https://orcid.org/0000-0003-4281-5331"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhijun Zhang","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":1.4647,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.8106263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"4","first_page":"1831","last_page":"1868"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9993000030517578,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9993000030517578,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.7766410112380981},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6857314109802246},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6077957153320312},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.6001153588294983},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5957146883010864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5829105377197266},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5530468225479126},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4921700358390808},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4916074872016907},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.46231114864349365},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.4279368817806244},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4256807565689087},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3533482551574707},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09947246313095093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7766410112380981},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6857314109802246},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6077957153320312},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.6001153588294983},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5957146883010864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5829105377197266},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5530468225479126},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4921700358390808},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4916074872016907},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.46231114864349365},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.4279368817806244},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4256807565689087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3533482551574707},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09947246313095093},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1107358","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1107358","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G532884643","display_name":null,"funder_award_id":"11571295","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6614942586","display_name":null,"funder_award_id":"11071185","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7933980107","display_name":"\u4e0d\u53d8\u96c6\u7406\u8bba\u53ca\u5176\u5e94\u7528\u4e2d\u82e5\u5e72\u95ee\u9898\u7684\u7814\u7a76","funder_award_id":"11471240","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W162901799","https://openalex.org/W1137405697","https://openalex.org/W1541936521","https://openalex.org/W1692273766","https://openalex.org/W1972072792","https://openalex.org/W1972441954","https://openalex.org/W1980434682","https://openalex.org/W1983797254","https://openalex.org/W1988768450","https://openalex.org/W1991313639","https://openalex.org/W1993344314","https://openalex.org/W2001694632","https://openalex.org/W2009033855","https://openalex.org/W2012067357","https://openalex.org/W2017053220","https://openalex.org/W2025950519","https://openalex.org/W2026851136","https://openalex.org/W2044786721","https://openalex.org/W2053916476","https://openalex.org/W2065477927","https://openalex.org/W2071506354","https://openalex.org/W2073971363","https://openalex.org/W2097953181","https://openalex.org/W2139507051","https://openalex.org/W2217855465","https://openalex.org/W2477580116","https://openalex.org/W2491364086","https://openalex.org/W2591663390"],"related_works":["https://openalex.org/W2404180431","https://openalex.org/W2803928976","https://openalex.org/W2072163537","https://openalex.org/W2348340245","https://openalex.org/W3097933399","https://openalex.org/W2560127293","https://openalex.org/W2546487931","https://openalex.org/W37064175","https://openalex.org/W2033303058","https://openalex.org/W2364686153"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"concerned":[3],"with":[4,83],"dynamic":[5,34,60],"bifurcation":[6,35,61],"from":[7,36,62],"infinity":[8,37,63],"and":[9,28,103],"multiplicity":[10,105],"of":[11,41,64,106,109],"stationary":[12,107],"solutions":[13,108],"for":[14],"nonlinear":[15],"evolution":[16,65],"equations":[17,66],"near":[18,112],"resonance.":[19],"First,":[20],"we":[21,53,71],"prove":[22],"some":[23],"new":[24],"global":[25],"continuation":[26],"results":[27],"establish":[29],"a":[30],"general":[31],"theorem":[32],"on":[33,44,58,75,99],"in":[38,67],"the":[39,59,76,84,91,100,104,110],"framework":[40],"local":[42],"semiflows":[43],"metric":[45],"spaces.":[46,69],"Then,":[47],"by":[48],"applying":[49],"these":[50],"abstract":[51],"results,":[52],"derive":[54],"more":[55],"precise":[56],"descriptions":[57],"Banach":[68],"Finally,":[70],"focus":[72],"our":[73],"attention":[74],"parabolic":[77],"equation":[78,111],"$u_t-\\Delta":[79],"u={\\lambda}":[80],"u+f(x,u)$":[81],"associated":[82],"Dirichlet":[85],"boundary":[86],"condition,":[87],"where":[88],"$f$":[89],"satisfies":[90],"appropriate":[92],"Landesman--Lazer":[93],"type":[94],"condition.":[95],"A":[96],"detailed":[97],"discussion":[98],"dynamical":[101],"behavior":[102],"resonance":[113],"will":[114],"be":[115],"presented.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}