{"id":"https://openalex.org/W1970801189","doi":"https://doi.org/10.1016/s0096-3003(99)00002-8","title":"A monotone approximation for a nonlinear nonautonomous size-structured population model","display_name":"A monotone approximation for a nonlinear nonautonomous size-structured population model","publication_year":2000,"publication_date":"2000-02-01","ids":{"openalex":"https://openalex.org/W1970801189","doi":"https://doi.org/10.1016/s0096-3003(99)00002-8","mag":"1970801189"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(99)00002-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(99)00002-8","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"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 and Computation","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/A5088755459","display_name":"Azmy S. Ackleh","orcid":"https://orcid.org/0000-0002-5774-2385"},"institutions":[{"id":"https://openalex.org/I8616870","display_name":"Southwestern University","ror":"https://ror.org/05gj63w50","country_code":"US","type":"education","lineage":["https://openalex.org/I8616870"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Azmy S. Ackleh","raw_affiliation_strings":["Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA","Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA","institution_ids":["https://openalex.org/I8616870"]},{"raw_affiliation_string":"Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA#TAB#","institution_ids":["https://openalex.org/I8616870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076621992","display_name":"Keng Deng","orcid":null},"institutions":[{"id":"https://openalex.org/I8616870","display_name":"Southwestern University","ror":"https://ror.org/05gj63w50","country_code":"US","type":"education","lineage":["https://openalex.org/I8616870"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Keng Deng","raw_affiliation_strings":["Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA","Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA","institution_ids":["https://openalex.org/I8616870"]},{"raw_affiliation_string":"Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA#TAB#","institution_ids":["https://openalex.org/I8616870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088755459"],"corresponding_institution_ids":["https://openalex.org/I8616870"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.6528,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.84677257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"108","issue":"2-3","first_page":"103","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9975000023841858,"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":0.9926999807357788,"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/monotone-polygon","display_name":"Monotone polygon","score":0.8109419345855713},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7500931024551392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7425865530967712},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6243507862091064},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6219423413276672},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5869328379631042},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.48664626479148865},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46765822172164917},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.4443919360637665},{"id":"https://openalex.org/keywords/population-model","display_name":"Population model","score":0.4282752275466919},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34160804748535156},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.34058648347854614},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30976933240890503},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07831215858459473}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8109419345855713},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7500931024551392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7425865530967712},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6243507862091064},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6219423413276672},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5869328379631042},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.48664626479148865},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46765822172164917},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.4443919360637665},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.4282752275466919},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34160804748535156},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.34058648347854614},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30976933240890503},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07831215858459473},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0096-3003(99)00002-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(99)00002-8","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"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 and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W621234224","https://openalex.org/W2000843180","https://openalex.org/W2019935627","https://openalex.org/W2047830843","https://openalex.org/W2050481397","https://openalex.org/W2056612112","https://openalex.org/W2217869637","https://openalex.org/W2482632963","https://openalex.org/W3022664448","https://openalex.org/W4251161845"],"related_works":["https://openalex.org/W2903488900","https://openalex.org/W2031309086","https://openalex.org/W2363311011","https://openalex.org/W1997932535","https://openalex.org/W2010049312","https://openalex.org/W2560766380","https://openalex.org/W2963771406","https://openalex.org/W2010521233","https://openalex.org/W2169403347","https://openalex.org/W2152819099"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}