{"id":"https://openalex.org/W2913307583","doi":"https://doi.org/10.1137/18m1174143","title":"Finite-Time and Fixed-Time Consensus of Multiagent Networks with Pinning Control and Noise Perturbation","display_name":"Finite-Time and Fixed-Time Consensus of Multiagent Networks with Pinning Control and Noise Perturbation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2913307583","doi":"https://doi.org/10.1137/18m1174143","mag":"2913307583"},"language":"en","primary_location":{"id":"doi:10.1137/18m1174143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1174143","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","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/A5003822957","display_name":"Yongzheng Sun","orcid":"https://orcid.org/0000-0001-9504-5663"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"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"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN","GB"],"is_corresponding":true,"raw_author_name":"Yongzheng Sun","raw_affiliation_strings":["\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100382436","display_name":"Wang Li","orcid":"https://orcid.org/0000-0003-2221-0626"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"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","GB"],"is_corresponding":false,"raw_author_name":"Wang Li","raw_affiliation_strings":["\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084189848","display_name":"Hongjun Shi","orcid":"https://orcid.org/0000-0001-7154-8004"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"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"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Hongjun Shi","raw_affiliation_strings":["\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China"],"affiliations":[{"raw_affiliation_string":"\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020124056","display_name":"Donghua Zhao","orcid":"https://orcid.org/0000-0002-4959-2647"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"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","GB"],"is_corresponding":false,"raw_author_name":"Donghua Zhao","raw_affiliation_strings":["\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China"],"affiliations":[{"raw_affiliation_string":"\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062771810","display_name":"Sandro Azaele","orcid":"https://orcid.org/0000-0002-5153-4833"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"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"]},{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Sandro Azaele","raw_affiliation_strings":["\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"\\S School of Mathematics,University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"\\dagger School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Peo-ple's Republic of China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"\\ddagger School of Mathematical Sciences, Research Center for Nonlinear Sciences, Fudan University, Shanghai 200433, People's Republic of China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5003822957"],"corresponding_institution_ids":["https://openalex.org/I130828816","https://openalex.org/I24943067","https://openalex.org/I25757504"],"apc_list":null,"apc_paid":null,"fwci":3.5379,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.93265089,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"79","issue":"1","first_page":"111","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/laplacian-matrix","display_name":"Laplacian matrix","score":0.6069201231002808},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5853252410888672},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4665757119655609},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4470304846763611},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.428314208984375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42528727650642395},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4199432134628296},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4197671115398407},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.410856693983078},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37947651743888855},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.3707389831542969},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34592652320861816},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23811271786689758},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2149142026901245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07253167033195496}],"concepts":[{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6069201231002808},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5853252410888672},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4665757119655609},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4470304846763611},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.428314208984375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42528727650642395},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4199432134628296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4197671115398407},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.410856693983078},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37947651743888855},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.3707389831542969},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34592652320861816},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23811271786689758},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2149142026901245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07253167033195496},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m1174143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1174143","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.whiterose.ac.uk:139979","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400854","display_name":"White Rose Research Online (University of Leeds, The University of Sheffield, University of York)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800616092","host_organization_name":"White Rose University Consortium","host_organization_lineage":["https://openalex.org/I2800616092"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:www.research.unipd.it:11577/3326166","is_oa":false,"landing_page_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1174143","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.9100000262260437}],"awards":[{"id":"https://openalex.org/G2728450828","display_name":null,"funder_award_id":"11711530203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6163602653","display_name":null,"funder_award_id":"IE161252","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G7481948742","display_name":null,"funder_award_id":"2017XKZD11","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7876768630","display_name":null,"funder_award_id":"61403393","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8516247378","display_name":null,"funder_award_id":"2017M621860","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1199106222","https://openalex.org/W1901170308","https://openalex.org/W1964501894","https://openalex.org/W1970847130","https://openalex.org/W1975318518","https://openalex.org/W1975387445","https://openalex.org/W1988837728","https://openalex.org/W1997637758","https://openalex.org/W1999040016","https://openalex.org/W2000149165","https://openalex.org/W2001591053","https://openalex.org/W2008620264","https://openalex.org/W2015113370","https://openalex.org/W2015410655","https://openalex.org/W2040840525","https://openalex.org/W2041833126","https://openalex.org/W2062692785","https://openalex.org/W2076081546","https://openalex.org/W2088473973","https://openalex.org/W2105850748","https://openalex.org/W2107396783","https://openalex.org/W2172143163","https://openalex.org/W2190271618","https://openalex.org/W2254624766","https://openalex.org/W2315330171","https://openalex.org/W2501147241","https://openalex.org/W2549542871","https://openalex.org/W2550187414","https://openalex.org/W2567252217","https://openalex.org/W2576016493","https://openalex.org/W2581282721","https://openalex.org/W2767959255","https://openalex.org/W2962871882","https://openalex.org/W2963465894","https://openalex.org/W3037683188"],"related_works":["https://openalex.org/W2784200061","https://openalex.org/W2784026553","https://openalex.org/W2511063373","https://openalex.org/W2333731806","https://openalex.org/W3127518712","https://openalex.org/W3096674331","https://openalex.org/W3088852461","https://openalex.org/W2113824758","https://openalex.org/W2335243741","https://openalex.org/W3085903267"],"abstract_inverted_index":{"In":[0,20],"this":[1],"paper":[2],"we":[3],"investigate":[4],"the":[5,24,36,42,64,72,78,85,93,96,103,107,112,118,125,135,147,150],"finite-time":[6,25,44,108,119,136],"and":[7,17,26,45,60,74,120,124,137],"fixed-time":[8,27,46,113,121,138],"consensus":[9,37,114],"problems":[10],"of":[11,55,67,84,149],"multiagent":[12],"networks":[13],"with":[14,35,95,102],"pinning":[15,30,40],"control":[16,50],"noise":[18],"perturbation.":[19],"order":[21],"to":[22,49,133,145],"reach":[23],"consensus,":[28],"several":[29],"protocols":[31,38,47,76,94],"are":[32,131,143],"proposed.":[33],"Compared":[34],"without":[39],"control,":[41],"proposed":[43],"need":[48],"only":[51],"a":[52,81],"small":[53],"fraction":[54],"agents,":[56],"which":[57],"is":[58],"practical":[59],"has":[61],"advantages":[62],"from":[63],"physical":[65],"viewpoint":[66],"energy":[68],"consumption.":[69],"More":[70],"specifically,":[71],"deterministic":[73],"stochastic":[75],"include":[77],"graph":[79,87,99,104,127],"$(p+1)$-Laplacian,":[80],"nonlinear":[82],"generalization":[83],"standard":[86,97],"Laplacian.":[88],"We":[89],"show":[90],"that,":[91],"unlike":[92],"(linear)":[98],"Laplacian,":[100],"those":[101],"$(p+1)$-Laplacian":[105],"solve":[106],"as":[109,111],"well":[110],"problems.":[115],"By":[116],"using":[117],"stability":[122],"theory":[123],"algebra":[126],"theory,":[128],"sufficient":[129],"conditions":[130],"established":[132],"ensure":[134],"consensus.":[139],"Finally,":[140],"numerical":[141],"simulations":[142],"presented":[144],"illustrate":[146],"correctness":[148],"theoretical":[151],"results.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}