{"id":"https://openalex.org/W4214737809","doi":"https://doi.org/10.1137/20m1383380","title":"On Solving Semilinear Singularly Perturbed Neumann Problems for Multiple Solutions","display_name":"On Solving Semilinear Singularly Perturbed Neumann Problems for Multiple Solutions","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W4214737809","doi":"https://doi.org/10.1137/20m1383380"},"language":"en","primary_location":{"id":"doi:10.1137/20m1383380","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1383380","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5108781250","display_name":"Ziqing Xie","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ziqing Xie","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025178510","display_name":"Yongjun Yuan","orcid":"https://orcid.org/0000-0002-7838-5479"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongjun Yuan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017633979","display_name":"Jianxin Zhou","orcid":"https://orcid.org/0000-0003-2111-2127"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianxin Zhou","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108781250"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9274,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67082485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"44","issue":"1","first_page":"A501","last_page":"A523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9991000294685364,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9987999796867371,"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":0.8537060022354126},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5767461657524109},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5707311630249023},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5132948756217957},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5102028846740723},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.48500773310661316},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.4820202589035034},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.47214677929878235},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4523636996746063},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44313088059425354},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.4389115571975708},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.4352276921272278},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4122595489025116},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22045189142227173},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18041133880615234},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08670687675476074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0761924684047699}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8537060022354126},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5767461657524109},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5707311630249023},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5132948756217957},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5102028846740723},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.48500773310661316},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.4820202589035034},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.47214677929878235},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4523636996746063},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44313088059425354},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.4389115571975708},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.4352276921272278},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4122595489025116},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22045189142227173},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18041133880615234},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08670687675476074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0761924684047699},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1383380","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1383380","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3307230641","display_name":null,"funder_award_id":"11971007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4916733487","display_name":null,"funder_award_id":"11771138","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G583420295","display_name":null,"funder_award_id":"18K025","funder_id":"https://openalex.org/F4320311213","funder_display_name":"Education Department of Hunan Province"},{"id":"https://openalex.org/G6302447807","display_name":null,"funder_award_id":"11601148","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320311213","display_name":"Education Department of Hunan Province","ror":"https://ror.org/05ckg3w11"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1483681777","https://openalex.org/W1505542423","https://openalex.org/W1796285435","https://openalex.org/W1967676806","https://openalex.org/W1978158875","https://openalex.org/W1994880182","https://openalex.org/W1996866305","https://openalex.org/W2001629516","https://openalex.org/W2003539068","https://openalex.org/W2003629838","https://openalex.org/W2005655499","https://openalex.org/W2007066944","https://openalex.org/W2008820258","https://openalex.org/W2012861268","https://openalex.org/W2014863630","https://openalex.org/W2023444505","https://openalex.org/W2025472770","https://openalex.org/W2025847892","https://openalex.org/W2028665571","https://openalex.org/W2030004448","https://openalex.org/W2034145387","https://openalex.org/W2049152374","https://openalex.org/W2054671813","https://openalex.org/W2057568191","https://openalex.org/W2065376268","https://openalex.org/W2075018793","https://openalex.org/W2085123496","https://openalex.org/W2089840306","https://openalex.org/W2091248801","https://openalex.org/W2091344274","https://openalex.org/W2092191962","https://openalex.org/W2121305176","https://openalex.org/W2129632677","https://openalex.org/W2883821673"],"related_works":["https://openalex.org/W2016058626","https://openalex.org/W2474724840","https://openalex.org/W2895916002","https://openalex.org/W1814049089","https://openalex.org/W1977348009","https://openalex.org/W2369683208","https://openalex.org/W1601883103","https://openalex.org/W2593550064","https://openalex.org/W2034624307","https://openalex.org/W2068336074"],"abstract_inverted_index":{"Based":[0],"on":[1],"the":[2,30,38,51,113],"analysis":[3],"of":[4,10,42,54,124,127],"bifurcation":[5],"points":[6,86],"and":[7,60,67,83,94,102,118],"Morse":[8],"indices":[9],"trivial":[11],"solutions":[12,45,57],"at":[13],"any":[14],"perturbation":[15,33,115],"value":[16,25,34,116],"for":[17],"a":[18,49,95],"general":[19],"semilinear":[20],"singularly":[21],"perturbed":[22],"Neumann":[23],"boundary":[24],"problem,":[26],"in":[27],"this":[28],"paper,":[29],"exact":[31],"critical":[32,114],"$\\varepsilon_c$":[35,117],"which":[36],"determines":[37],"existence":[39],"or":[40],"nonexistence":[41],"nontrivial":[43,55],"positive":[44,56],"is":[46,58,75],"obtained.":[47],"As":[48],"result,":[50],"generating":[52],"process":[53],"studied":[59],"further":[61],"used":[62],"to":[63,79,98,111],"guide":[64],"algorithm":[65],"design":[66],"numerical":[68,107],"computation.":[69],"An":[70],"improved":[71],"local":[72,91,104],"minimax":[73],"method":[74,97],"then":[76],"proposed":[77],"accordingly":[78],"compute":[80],"both":[81],"M-type":[82],"W-type":[84],"saddle":[85],"by":[87],"using":[88],"an":[89],"adaptive":[90],"refinement":[92],"strategy":[93],"Newton":[96],"overcome":[99],"singularity":[100],"difficulty":[101],"accelerate":[103],"convergence.":[105],"Extensive":[106],"results":[108],"are":[109],"reported":[110],"justify":[112],"investigate":[119],"some":[120],"interesting":[121],"solution":[122],"properties":[123],"different":[125],"types":[126],"problems.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}