{"id":"https://openalex.org/W4312205129","doi":"https://doi.org/10.1002/mma.8979","title":"On non\u2010local elliptic equations with sublinear nonlinearities involving an eigenvalue problem","display_name":"On non\u2010local elliptic equations with sublinear nonlinearities involving an eigenvalue problem","publication_year":2022,"publication_date":"2022-12-23","ids":{"openalex":"https://openalex.org/W4312205129","doi":"https://doi.org/10.1002/mma.8979"},"language":"en","primary_location":{"id":"doi:10.1002/mma.8979","doi":"https://doi.org/10.1002/mma.8979","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mma.8979","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4312205129"],"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/A5101682082","display_name":"Ching\u2010yu Chen","orcid":"https://orcid.org/0000-0002-1656-3436","observed_orcids":["https://orcid.org/0000-0002-1656-3436"]},"institutions":[{"id":"https://openalex.org/I192168892","display_name":"National University of Kaohsiung","ror":"https://ror.org/013zjb662","country_code":"TW","type":"education","lineage":["https://openalex.org/I192168892"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Ching\u2010yu Chen","raw_affiliation_strings":["Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811 Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811 Taiwan","institution_ids":["https://openalex.org/I192168892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004863623","display_name":"Yueh\u2010Cheng Kuo","orcid":"https://orcid.org/0000-0003-2387-6913","observed_orcids":["https://orcid.org/0000-0003-2387-6913"]},"institutions":[{"id":"https://openalex.org/I192168892","display_name":"National University of Kaohsiung","ror":"https://ror.org/013zjb662","country_code":"TW","type":"education","lineage":["https://openalex.org/I192168892"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yueh\u2010cheng Kuo","raw_affiliation_strings":["Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811 Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811 Taiwan","institution_ids":["https://openalex.org/I192168892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039103194","display_name":"Kuan\u2010Hsiang Wang","orcid":"https://orcid.org/0000-0003-1570-7749","observed_orcids":["https://orcid.org/0000-0003-1570-7749"]},"institutions":[{"id":"https://openalex.org/I91807558","display_name":"National Cheng Kung University","ror":"https://ror.org/01b8kcc49","country_code":"TW","type":"education","lineage":["https://openalex.org/I91807558"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Kuan\u2010Hsiang Wang","raw_affiliation_strings":["Department of Mathematics, National Cheng Kung University, Tainan, Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-1570-7749","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Cheng Kung University, Tainan, Taiwan","institution_ids":["https://openalex.org/I91807558"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036558482","display_name":"Tsung\u2010fang Wu","orcid":"https://orcid.org/0000-0003-4945-652X","observed_orcids":["https://orcid.org/0000-0003-4945-652X"]},"institutions":[{"id":"https://openalex.org/I192168892","display_name":"National University of Kaohsiung","ror":"https://ror.org/013zjb662","country_code":"TW","type":"education","lineage":["https://openalex.org/I192168892"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Tsung\u2010fang Wu","raw_affiliation_strings":["Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811 Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-4945-652X","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811 Taiwan","institution_ids":["https://openalex.org/I192168892"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036558482"],"corresponding_institution_ids":["https://openalex.org/I192168892"],"apc_list":{"value":4400,"currency":"USD","value_usd":4400},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"6","first_page":"7454","last_page":"7465"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9901999831199646,"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":0.9901999831199646,"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":0.007799999788403511,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kirchhoff-type-equations","display_name":"Kirchhoff-type equations","score":0.8790000081062317},{"id":"https://openalex.org/keywords/sublinear-nonlinearity","display_name":"sublinear nonlinearity","score":0.9300000071525574},{"id":"https://openalex.org/keywords/dirichlet-boundary-conditions","display_name":"Dirichlet boundary conditions","score":0.8740000128746033},{"id":"https://openalex.org/keywords/eigenvalue-problem","display_name":"eigenvalue problem","score":0.7149999737739563},{"id":"https://openalex.org/keywords/bifurcation-from-infinity","display_name":"bifurcation from infinity","score":0.9150000214576721},{"id":"https://openalex.org/keywords/positive-solutions","display_name":"positive solutions","score":0.8550000190734863},{"id":"https://openalex.org/keywords/multiple-solutions","display_name":"multiplicity of solutions","score":0.7549999952316284},{"id":"https://openalex.org/keywords/principal-eigenvalue","display_name":"principal eigenvalue","score":0.7110000252723694},{"id":"https://openalex.org/keywords/nonlocal-effects","display_name":"nonlocal effects","score":0.5929999947547913}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9192367196083069},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7563406825065613},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.744341254234314},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6437171697616577},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6389291882514954},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5562039613723755},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5158478617668152},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5074815154075623},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.48670151829719543},{"id":"https://openalex.org/C94242865","wikidata":"https://www.wikidata.org/wiki/Q5365788","display_name":"Elliptic boundary value problem","level":4,"score":0.46744880080223083},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.42706722021102905},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3875004053115845},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.1447545289993286},{"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:10.1002/mma.8979","doi":"https://doi.org/10.1002/mma.8979","is_oa":false,"landing_page_url":"https://doi.org/10.1002/mma.8979","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6780022626","display_name":"Nodal Solutions for the Non-Autonomous Schr\u00f6dinger-Poisson System","funder_award_id":"MOST108-2115-M390-007-MY2","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"},{"id":"https://openalex.org/G888609995","display_name":null,"funder_award_id":"108-2811-M-390-500","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"}],"funders":[{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W93792870","https://openalex.org/W1560787783","https://openalex.org/W1973748816","https://openalex.org/W1981288703","https://openalex.org/W1982543799","https://openalex.org/W1996518052","https://openalex.org/W2001383411","https://openalex.org/W2002699081","https://openalex.org/W2007261596","https://openalex.org/W2036198852","https://openalex.org/W2056249562","https://openalex.org/W2060691357","https://openalex.org/W2065699653","https://openalex.org/W2315618180","https://openalex.org/W2328171856","https://openalex.org/W2489808042","https://openalex.org/W2735383720","https://openalex.org/W3216245756"],"related_works":["https://openalex.org/W2732743443","https://openalex.org/W2461737231","https://openalex.org/W2330341720","https://openalex.org/W2519029769","https://openalex.org/W2770740261","https://openalex.org/W4417516515","https://openalex.org/W3175317036","https://openalex.org/W4398139241","https://openalex.org/W2561286636","https://openalex.org/W2996122971"],"abstract_inverted_index":{"A":[0],"non\u2010local":[1,25,70,123],"elliptic":[2,116],"equation":[3],"of":[4,32,60,68,102,108,114,121],"Kirchhoff\u2010type":[5],"for":[6,13,45,89,99],"with":[7,23,93,112],"Dirichlet":[8],"boundary":[9],"conditions":[10,129],"is":[11,19,56,86],"investigated":[12],"the":[14,24,57,61,69,109,115,119,122,126],"cases":[15],"where":[16],".":[17,64,90,103],"It":[18],"well":[20],"known":[21],"that":[22],"effect":[26],"removed":[27],"and":[28,39,80],",":[29],"a":[30,66],"branch":[31],"positive":[33,41,84,95],"solutions":[34,96],"bifurcates":[35],"from":[36,78],"infinity":[37],"at":[38,81],"no":[40,76],"solution":[42,85],"exists":[43],"whenever":[44],"some":[46],"(see":[47],"K.":[48],"J.":[49],"Brown,":[50],"Calc.":[51],"Var.":[52],"22,":[53],"483\u2010494,":[54],"2005),where":[55],"principal":[58],"eigenvalue":[59],"linear":[62],"problem":[63,117],"As":[65],"consequence":[67],"effect,":[71],"our":[72],"analysis":[73],"has":[74],"found":[75,98],"bifurcation":[77],"infinity,":[79],"least":[82],"one":[83],"always":[87],"permitted":[88],"Moreover,":[91],"regions":[92],"three":[94],"are":[97,105],"small":[100],"value":[101],"Comparisons":[104],"also":[106],"made":[107],"results":[110],"here":[111],"those":[113],"in":[118],"absence":[120],"term":[124],"under":[125],"same":[127],"prescribed":[128],"using":[130],"numerical":[131],"simulations.":[132]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2023-01-04T00:00:00"}