{"id":"https://openalex.org/W2013387710","doi":"https://doi.org/10.1080/10586458.2006.10128944","title":"Nonlinear Elliptic Partial Difference Equations on Graphs","display_name":"Nonlinear Elliptic Partial Difference Equations on Graphs","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2013387710","doi":"https://doi.org/10.1080/10586458.2006.10128944","mag":"2013387710"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2006.10128944","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2006.10128944","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental 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/A5080317531","display_name":"John M. Neuberger","orcid":null},"institutions":[{"id":"https://openalex.org/I203172682","display_name":"Northern Arizona University","ror":"https://ror.org/0272j5188","country_code":"US","type":"education","lineage":["https://openalex.org/I203172682"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John M. Neuberger","raw_affiliation_strings":["Department of Mathematics and Statistics, Northern Arizona University, Box 5717, Flagstaff, AZ 86011","Mathematics and Statistics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Northern Arizona University, Box 5717, Flagstaff, AZ 86011","institution_ids":["https://openalex.org/I203172682"]},{"raw_affiliation_string":"Mathematics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080317531"],"corresponding_institution_ids":["https://openalex.org/I203172682"],"apc_list":null,"apc_paid":null,"fwci":2.2543,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.85473378,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","issue":"1","first_page":"91","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9947999715805054,"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":0.9947999715805054,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9617999792098999,"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/mathematics","display_name":"Mathematics","score":0.8831431269645691},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.742233395576477},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6103112697601318},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5650168061256409},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5267759561538696},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4186103343963623},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.4143421947956085},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38685303926467896},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3759167492389679},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3592919111251831},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30902108550071716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8831431269645691},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.742233395576477},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6103112697601318},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5650168061256409},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5267759561538696},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4186103343963623},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4143421947956085},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38685303926467896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3759167492389679},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3592919111251831},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30902108550071716},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2006.10128944","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2006.10128944","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1150476907","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1150476907","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.450","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.expmath.org/expmath/volumes/15/15.1/Neuberger.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.73.6526","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.6526","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://jan.ucc.nau.edu/~jmn3/graphs/as_submitted_graph.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W247697463","https://openalex.org/W1483726821","https://openalex.org/W1506690472","https://openalex.org/W1531642383","https://openalex.org/W1578099820","https://openalex.org/W1960491414","https://openalex.org/W1965778005","https://openalex.org/W1967468633","https://openalex.org/W1981288703","https://openalex.org/W1984241241","https://openalex.org/W1984781443","https://openalex.org/W2018239539","https://openalex.org/W2039350867","https://openalex.org/W2041069004","https://openalex.org/W2053630489","https://openalex.org/W2058270372","https://openalex.org/W2059056989","https://openalex.org/W2061541719","https://openalex.org/W2064219620","https://openalex.org/W2084688031","https://openalex.org/W2086190927","https://openalex.org/W2095271260","https://openalex.org/W2121174441","https://openalex.org/W2141521843","https://openalex.org/W2160318338","https://openalex.org/W2161576964","https://openalex.org/W2572321817","https://openalex.org/W2602547166","https://openalex.org/W3038830718"],"related_works":["https://openalex.org/W2682190590","https://openalex.org/W935007796","https://openalex.org/W97241627","https://openalex.org/W2358589552","https://openalex.org/W2985622559","https://openalex.org/W4366197524","https://openalex.org/W2066764747","https://openalex.org/W2027741235","https://openalex.org/W2488373638","https://openalex.org/W4254213601"],"abstract_inverted_index":{"This":[0],"article":[1],"furthers":[2],"the":[3,23,41,45,61,73,83,89,121,124],"study":[4],"of":[5,75,88],"nonlinear":[6,102],"elliptic":[7,25],"partial":[8,26,62],"difference":[9,27],"equations":[10],"(PdE)":[11],"on":[12,32,44],"graphs.":[13],"We":[14,48],"seek":[15],"solutions":[16,77,79],"u":[17],":":[18],"V":[19],"\u2192":[20],"\u211d":[21],"to":[22,52,123],"semilinear":[24],"equation":[28,64],"-Lu+\u0192(u)":[29],"=":[30,36,67,112],"0":[31],"a":[33],"graph":[34,46],"G":[35],"(V,E),":[37],"where":[38],"L":[39],"is":[40],"(negative)":[42],"Laplacian":[43],"G.":[47],"extend":[49],"techniques":[50],"used":[51],"prove":[53,72],"existence":[54,74],"theorems":[55],"and":[56,78,95,106,119],"derive":[57],"numerical":[58],"algorithms":[59,98],"for":[60,99],"differential":[63],"(PDE)":[65],"\u0394u+\u0192(u)":[66],"0.":[68],"In":[69],"particular,":[70],"we":[71,104,115],"sign-changing":[76],"with":[80],"symmetry":[81],"in":[82],"superlinear":[84],"case.":[85],"Developing":[86],"variants":[87],"mountain":[90,93],"pass,":[91,94],"modified":[92],"gradient":[96],"Newton\u2013Galerkin":[97],"our":[100],"discrete":[101],"problem,":[103],"compute":[105],"describe":[107],"many":[108],"solutions.":[109],"Letting":[110],"\u0192":[111],"\u0192(\u03bb,":[113],"u),":[114],"construct":[116],"bifurcation":[117],"diagrams":[118],"relate":[120],"results":[122],"developed":[125],"theory.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
