{"id":"https://openalex.org/W4285106956","doi":"https://doi.org/10.3934/era.2022137","title":"Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems","display_name":"Existence and multiplicity of nontrivial solutions to discrete elliptic Dirichlet problems","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4285106956","doi":"https://doi.org/10.3934/era.2022137"},"language":"en","primary_location":{"id":"doi:10.3934/era.2022137","doi":"https://doi.org/10.3934/era.2022137","is_oa":true,"landing_page_url":"https://doi.org/10.3934/era.2022137","pdf_url":null,"source":{"id":"https://openalex.org/S4210240239","display_name":"Electronic Research Archive","issn_l":"2688-1594","issn":["2688-1594"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Research Archive","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3934/era.2022137","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100600269","display_name":"Yuhua Long","orcid":"https://orcid.org/0000-0002-0264-1261","observed_orcids":["https://orcid.org/0000-0002-0264-1261"]},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuhua Long","raw_affiliation_strings":["Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou 510006, China","School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100356925","display_name":"Huan Zhang","orcid":"https://orcid.org/0000-0001-6201-7287","observed_orcids":["https://orcid.org/0000-0001-6201-7287"]},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Huan Zhang","raw_affiliation_strings":["Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou 510006, China","School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangzhou University, Guangzhou Center for Applied Mathematics, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100356925"],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":{"value":1000,"currency":"USD","value_usd":1000},"apc_paid":{"value":1000,"currency":"USD","value_usd":1000},"fwci":1.7182,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82638173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"30","issue":"7","first_page":"2681","last_page":"2699"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.989300012588501,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.989300012588501,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.005799999926239252,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/nontrivial-solutions","display_name":"nontrivial solutions","score":0.9729999899864197},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.8610000014305115},{"id":"https://openalex.org/keywords/multiple-solutions","display_name":"multiplicity of solutions","score":0.9990000128746033},{"id":"https://openalex.org/keywords/discrete-laplacian","display_name":"discrete Laplacian","score":0.8050000071525574},{"id":"https://openalex.org/keywords/variational-methods","display_name":"variational methods","score":0.8100000023841858},{"id":"https://openalex.org/keywords/morse-theory","display_name":"Morse theory","score":0.9980000257492065}],"concepts":[{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.8439595699310303},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.7132200002670288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6513994932174683},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.647071123123169},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.5623710751533508},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45949888229370117},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42444437742233276},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.41299688816070557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3393442630767822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1306229829788208},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.04278102517127991},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/era.2022137","doi":"https://doi.org/10.3934/era.2022137","is_oa":true,"landing_page_url":"https://doi.org/10.3934/era.2022137","pdf_url":null,"source":{"id":"https://openalex.org/S4210240239","display_name":"Electronic Research Archive","issn_l":"2688-1594","issn":["2688-1594"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Research Archive","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d584cd0f853b4c3fb2361157a55cca87","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/d584cd0f853b4c3fb2361157a55cca87","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,"listed_in":[],"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":"Electronic Research Archive, Vol 30, Iss 7, Pp 2681-2699 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/era.2022137","doi":"https://doi.org/10.3934/era.2022137","is_oa":true,"landing_page_url":"https://doi.org/10.3934/era.2022137","pdf_url":null,"source":{"id":"https://openalex.org/S4210240239","display_name":"Electronic Research Archive","issn_l":"2688-1594","issn":["2688-1594"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Research Archive","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W650714123","https://openalex.org/W1575983931","https://openalex.org/W1973294555","https://openalex.org/W1977109057","https://openalex.org/W1986099574","https://openalex.org/W1995200952","https://openalex.org/W2017374973","https://openalex.org/W2021152503","https://openalex.org/W2021700372","https://openalex.org/W2128955195","https://openalex.org/W2141521843","https://openalex.org/W2168315991","https://openalex.org/W2618772921","https://openalex.org/W2624485921","https://openalex.org/W2751734715","https://openalex.org/W2793559259","https://openalex.org/W2885091715","https://openalex.org/W2903415972","https://openalex.org/W2923794764","https://openalex.org/W2976542242","https://openalex.org/W2990145405","https://openalex.org/W2990879582","https://openalex.org/W3049705855","https://openalex.org/W3089665028","https://openalex.org/W3134290676","https://openalex.org/W3164875402","https://openalex.org/W3178920604","https://openalex.org/W3209101168","https://openalex.org/W3216353394","https://openalex.org/W4221057965","https://openalex.org/W4221067062","https://openalex.org/W4224032119","https://openalex.org/W4226464084","https://openalex.org/W4285751554","https://openalex.org/W4300776790"],"related_works":["https://openalex.org/W1595332435","https://openalex.org/W2548670722","https://openalex.org/W3084339456","https://openalex.org/W1976948755","https://openalex.org/W2037435271","https://openalex.org/W2182193748","https://openalex.org/W1966769279","https://openalex.org/W2047313820","https://openalex.org/W2208124994","https://openalex.org/W2043692898"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,17],"study":[4],"discrete":[5],"elliptic":[6],"Dirichlet":[7],"problems.":[8],"Applying":[9],"a":[10],"variational":[11],"technique":[12],"together":[13],"with":[14],"Morse":[15],"theory,":[16],"establish":[18],"several":[19],"results":[20],"on":[21],"the":[22],"existence":[23],"and":[24,32],"multiplicity":[25],"of":[26],"nontrivial":[27],"solutions.":[28],"Finally,":[29],"two":[30],"examples":[31],"numerical":[33],"simulations":[34],"are":[35],"provided":[36],"to":[37],"illustrate":[38],"our":[39],"theoretical":[40],"results.":[41]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
