{"id":"https://openalex.org/W2057170938","doi":"https://doi.org/10.1016/s0893-9659(03)80044-7","title":"A necessary and sufficient condition for the existence of positive solutions of fourth-order singular boundary value problems","display_name":"A necessary and sufficient condition for the existence of positive solutions of fourth-order singular boundary value problems","publication_year":2003,"publication_date":"2003-04-01","ids":{"openalex":"https://openalex.org/W2057170938","doi":"https://doi.org/10.1016/s0893-9659(03)80044-7","mag":"2057170938"},"language":"en","primary_location":{"id":"doi:10.1016/s0893-9659(03)80044-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0893-9659(03)80044-7","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","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/A5078295917","display_name":"Zhaocai Hao","orcid":"https://orcid.org/0000-0002-7924-3325"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaocai Hao","raw_affiliation_strings":["Department of Mathematics Qufu Normal University Qufu, Shandong 273165, P.R. China","Department of Mathematics , Qufu Normal University , Qufu , Shandong , 273165 , P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Qufu Normal University Qufu, Shandong 273165, P.R. China","institution_ids":["https://openalex.org/I202126657"]},{"raw_affiliation_string":"Department of Mathematics , Qufu Normal University , Qufu , Shandong , 273165 , P. R. China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000389536","display_name":"Lishan Liu","orcid":"https://orcid.org/0000-0001-8541-1017"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lishan Liu","raw_affiliation_strings":["Department of Mathematics Qufu Normal University Qufu, Shandong 273165, P.R. China","Department of Mathematics , Qufu Normal University , Qufu , Shandong , 273165 , P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Qufu Normal University Qufu, Shandong 273165, P.R. China","institution_ids":["https://openalex.org/I202126657"]},{"raw_affiliation_string":"Department of Mathematics , Qufu Normal University , Qufu , Shandong , 273165 , P. R. China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111542030","display_name":"L. Debnath","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"L. Debnath","raw_affiliation_strings":["Department of Mathematics University of Texas-Pan American 1201 W. University Drive Edinburg, TX 78539, USA","Department of Mathematics, University of Texas - Pan American, 1201 W. University Drive, Edinburg, TX 78539, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Texas-Pan American 1201 W. University Drive Edinburg, TX 78539, USA","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, University of Texas - Pan American, 1201 W. University Drive, Edinburg, TX 78539, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000389536","https://openalex.org/A5111542030"],"corresponding_institution_ids":["https://openalex.org/I202126657"],"apc_list":{"value":3540,"currency":"USD","value_usd":3540},"apc_paid":null,"fwci":1.5224,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.79879631,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"3","first_page":"279","last_page":"285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9986000061035156,"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":0.9986000061035156,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9916999936103821,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9379559755325317},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.879260778427124},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.7035920023918152},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.6332199573516846},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5897760987281799},{"id":"https://openalex.org/keywords/fixed-point-index","display_name":"Fixed-point index","score":0.5874192118644714},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5812705755233765},{"id":"https://openalex.org/keywords/singular-solution","display_name":"Singular solution","score":0.5731488466262817},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5724655389785767},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.534489631652832},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4296637773513794},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37111371755599976}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9379559755325317},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.879260778427124},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.7035920023918152},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.6332199573516846},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5897760987281799},{"id":"https://openalex.org/C2780668686","wikidata":"https://www.wikidata.org/wiki/Q5456324","display_name":"Fixed-point index","level":3,"score":0.5874192118644714},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5812705755233765},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.5731488466262817},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5724655389785767},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.534489631652832},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4296637773513794},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37111371755599976},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0893-9659(03)80044-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0893-9659(03)80044-7","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1970375348","https://openalex.org/W1975221158","https://openalex.org/W1991252601","https://openalex.org/W2013527677","https://openalex.org/W2015002543","https://openalex.org/W2038697094","https://openalex.org/W2057340530","https://openalex.org/W2059518219","https://openalex.org/W2082355228","https://openalex.org/W2116041548","https://openalex.org/W2136404093","https://openalex.org/W2588009873","https://openalex.org/W4245024490","https://openalex.org/W6653885373"],"related_works":["https://openalex.org/W2388505395","https://openalex.org/W2345519532","https://openalex.org/W2384453108","https://openalex.org/W2941079155","https://openalex.org/W2378455712","https://openalex.org/W2221843812","https://openalex.org/W2023464650","https://openalex.org/W4388915104","https://openalex.org/W2160873128","https://openalex.org/W2090103360"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}