{"id":"https://openalex.org/W4281895462","doi":"https://doi.org/10.3390/sym14061141","title":"Multiplicity of Solutions for Quasilinear Differential Models Generated by Instantaneous and Non-Instantaneous Impulses","display_name":"Multiplicity of Solutions for Quasilinear Differential Models Generated by Instantaneous and Non-Instantaneous Impulses","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W4281895462","doi":"https://doi.org/10.3390/sym14061141"},"language":"en","primary_location":{"id":"doi:10.3390/sym14061141","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061141","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1141/pdf?version=1654075157","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/6/1141/pdf?version=1654075157","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041686457","display_name":"Tengfei Shen","orcid":"https://orcid.org/0000-0002-9016-3473"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tengfei Shen","raw_affiliation_strings":["School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112166153","display_name":"Wenbin Liu","orcid":"https://orcid.org/0000-0001-7065-8551"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenbin Liu","raw_affiliation_strings":["School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100441734","display_name":"Wei Zhang","orcid":"https://orcid.org/0000-0003-0003-0341"},"institutions":[{"id":"https://openalex.org/I184681353","display_name":"Anhui University of Science and Technology","ror":"https://ror.org/00q9atg80","country_code":"CN","type":"education","lineage":["https://openalex.org/I184681353"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zhang","raw_affiliation_strings":["School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China","institution_ids":["https://openalex.org/I184681353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041686457"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3556,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.46772814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"6","first_page":"1141","last_page":"1141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994000196456909,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/multiplicity","display_name":"Multiplicity (mathematics)","score":0.8350109457969666},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5016255378723145},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.45506733655929565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4549642503261566},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.41712889075279236},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3824029266834259},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3764230012893677},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3561570644378662},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2625928223133087},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07518473267555237}],"concepts":[{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.8350109457969666},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5016255378723145},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.45506733655929565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4549642503261566},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.41712889075279236},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3824029266834259},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3764230012893677},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3561570644378662},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2625928223133087},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07518473267555237},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14061141","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061141","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1141/pdf?version=1654075157","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:efbced44bb324b20be7f53fe8ba4956e","is_oa":true,"landing_page_url":"https://doaj.org/article/efbced44bb324b20be7f53fe8ba4956e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 6, p 1141 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/6/1141/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14061141","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":"Symmetry; Volume 14; Issue 6; Pages: 1141","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14061141","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061141","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1141/pdf?version=1654075157","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3444180157","display_name":null,"funder_award_id":"2019QNA05","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3741879925","display_name":null,"funder_award_id":"BK20190620","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G4629855149","display_name":null,"funder_award_id":"BK20190620","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281895462.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W134217836","https://openalex.org/W1987682875","https://openalex.org/W1997682518","https://openalex.org/W2006458524","https://openalex.org/W2015192593","https://openalex.org/W2023988079","https://openalex.org/W2029125428","https://openalex.org/W2030167963","https://openalex.org/W2050240106","https://openalex.org/W2055316229","https://openalex.org/W2058270372","https://openalex.org/W2073183458","https://openalex.org/W2273532493","https://openalex.org/W2292425095","https://openalex.org/W2608221280","https://openalex.org/W2611201473","https://openalex.org/W2792717123","https://openalex.org/W2898229012","https://openalex.org/W2921756308","https://openalex.org/W2966773443","https://openalex.org/W3132644331","https://openalex.org/W3194510291","https://openalex.org/W4229872608","https://openalex.org/W6991130631"],"related_works":["https://openalex.org/W4378765297","https://openalex.org/W4230581126","https://openalex.org/W2761548024","https://openalex.org/W2016521071","https://openalex.org/W2001367988","https://openalex.org/W2069384021","https://openalex.org/W4394867213","https://openalex.org/W1990308498","https://openalex.org/W1986629578","https://openalex.org/W3196781293"],"abstract_inverted_index":{"This":[0],"paper":[1],"aims":[2],"to":[3,60],"deal":[4],"with":[5],"the":[6,23,29,36,45,62,65],"multiplicity":[7],"of":[8,31,64],"weak":[9],"solutions":[10],"for":[11],"quasilinear":[12,37],"differential":[13],"models":[14],"generated":[15],"by":[16,35],"instantaneous":[17],"and":[18,27,50],"non-instantaneous":[19],"impulses.":[20],"By":[21],"establishing":[22],"new":[24,40],"variational":[25],"structure":[26],"overcoming":[28],"influence":[30],"impulsive":[32],"effects":[33],"brought":[34],"term,":[38],"some":[39,52],"results":[41],"are":[42],"acquired":[43],"via":[44],"gene":[46],"property,":[47],"which":[48],"extends":[49],"enriches":[51],"previous":[53],"results.":[54,67],"Moreover,":[55],"an":[56],"example":[57],"is":[58],"given":[59],"illustrate":[61],"conclusion":[63],"main":[66]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
