{"id":"https://openalex.org/W4293413746","doi":"https://doi.org/10.3390/axioms11090435","title":"Existence and Uniqueness of Solution to a Terminal Value Problem of First-Order Differential Equation","display_name":"Existence and Uniqueness of Solution to a Terminal Value Problem of First-Order Differential Equation","publication_year":2022,"publication_date":"2022-08-26","ids":{"openalex":"https://openalex.org/W4293413746","doi":"https://doi.org/10.3390/axioms11090435"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11090435","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090435","pdf_url":"https://www.mdpi.com/2075-1680/11/9/435/pdf?version=1663746570","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/9/435/pdf?version=1663746570","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030009466","display_name":"Yuqiang Feng","orcid":"https://orcid.org/0000-0002-1208-0509"},"institutions":[{"id":"https://openalex.org/I43922553","display_name":"Wuhan University of Science and Technology","ror":"https://ror.org/00e4hrk88","country_code":"CN","type":"education","lineage":["https://openalex.org/I43922553"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuqiang Feng","raw_affiliation_strings":["School of Science, Wuhan University of Science and Technology, Wuhan 430081, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Wuhan University of Science and Technology, Wuhan 430081, China","institution_ids":["https://openalex.org/I43922553"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113170645","display_name":"Pan Qian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qian Pan","raw_affiliation_strings":["Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China"],"affiliations":[{"raw_affiliation_string":"Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100619997","display_name":"Jun Jiang","orcid":"https://orcid.org/0000-0002-6116-5605"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun Jiang","raw_affiliation_strings":["Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China"],"affiliations":[{"raw_affiliation_string":"Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030009466"],"corresponding_institution_ids":["https://openalex.org/I43922553"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09009009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"9","first_page":"435","last_page":"435"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9988999962806702,"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":0.9986000061035156,"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":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8488650918006897},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7121107578277588},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.6918518543243408},{"id":"https://openalex.org/keywords/terminal","display_name":"Terminal (telecommunication)","score":0.6757796406745911},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5779343843460083},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5352794528007507},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.513295590877533},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5086361169815063},{"id":"https://openalex.org/keywords/terminal-value","display_name":"Terminal value","score":0.4803929924964905},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42353975772857666},{"id":"https://openalex.org/keywords/first-order","display_name":"First order","score":0.4125881791114807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41210728883743286},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3622914254665375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2043045163154602},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05308353900909424}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8488650918006897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7121107578277588},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.6918518543243408},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.6757796406745911},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5779343843460083},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5352794528007507},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.513295590877533},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5086361169815063},{"id":"https://openalex.org/C47096860","wikidata":"https://www.wikidata.org/wiki/Q575542","display_name":"Terminal value","level":4,"score":0.4803929924964905},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42353975772857666},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.4125881791114807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41210728883743286},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3622914254665375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2043045163154602},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05308353900909424},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C76087492","wikidata":"https://www.wikidata.org/wiki/Q1047352","display_name":"Cash management","level":3,"score":0.0},{"id":"https://openalex.org/C2778083465","wikidata":"https://www.wikidata.org/wiki/Q693464","display_name":"Cash","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11090435","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090435","pdf_url":"https://www.mdpi.com/2075-1680/11/9/435/pdf?version=1663746570","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:aa66c4f7a3c44fabbb41701ff2b5e0e5","is_oa":true,"landing_page_url":"https://doaj.org/article/aa66c4f7a3c44fabbb41701ff2b5e0e5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 9, p 435 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/9/435/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11090435","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 9; Pages: 435","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11090435","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090435","pdf_url":"https://www.mdpi.com/2075-1680/11/9/435/pdf?version=1663746570","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6241571742","display_name":null,"funder_award_id":"72031009","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4293413746.pdf","grobid_xml":"https://content.openalex.org/works/W4293413746.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1411309425","https://openalex.org/W2084243570","https://openalex.org/W2744653261","https://openalex.org/W2945310135","https://openalex.org/W3027949248","https://openalex.org/W3166918342"],"related_works":["https://openalex.org/W4230978976","https://openalex.org/W1999585122","https://openalex.org/W186744944","https://openalex.org/W2358913001","https://openalex.org/W2076832505","https://openalex.org/W2388576803","https://openalex.org/W3014294111","https://openalex.org/W2519231087","https://openalex.org/W4293413746","https://openalex.org/W2075335096"],"abstract_inverted_index":{"The":[0],"terminal":[1,20],"value":[2,21],"problem":[3,22],"of":[4,23,40,76],"differential":[5,26],"equations":[6],"has":[7],"an":[8,52,68],"important":[9],"application":[10,75],"background.":[11],"In":[12],"this":[13],"paper,":[14],"we":[15],"are":[16,31,49,59],"concerned":[17],"with":[18],"the":[19,35,43,64,74,77],"a":[24],"first-order":[25],"equation.":[27],"Some":[28],"sufficient":[29],"conditions":[30],"given":[32],"to":[33,42,61,72],"obtain":[34],"existence":[36],"and":[37,55],"uniqueness":[38],"results":[39],"solutions":[41],"problem.":[44],"Firstly,":[45],"some":[46],"comparison":[47],"lemmas":[48],"established;":[50],"secondly,":[51],"iterative":[53],"technique":[54],"fixed":[56],"point":[57],"method":[58],"used":[60],"set":[62],"up":[63],"main":[65,78],"results;":[66],"Finally,":[67],"example":[69],"is":[70],"provided":[71],"illustrate":[73],"results.":[79]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2022-08-29T00:00:00"}