{"id":"https://openalex.org/W2162144866","doi":null,"title":"Nodal Domains for the p-Laplacian","display_name":"Nodal Domains for the p-Laplacian","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2162144866","mag":"2162144866"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.649.8125","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.649.8125","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://campus.mst.edu/adsa/contents/v2n2p1.pdf","raw_type":"text"},"parent_works":[],"lineage":["https://openalex.org/W2162144866"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":[],"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/A5010876022","display_name":"Aomar Anane","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aomar Anane","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056294196","display_name":"Omar Chakrone","orcid":"https://orcid.org/0000-0002-2208-4220","observed_orcids":["https://orcid.org/0000-0002-2208-4220"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Omar Chakrone","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2208-4220","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Mohamed Filali","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohamed Filali","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061840876","display_name":"Belhadj Karim","orcid":"https://orcid.org/0000-0002-7455-5434","observed_orcids":["https://orcid.org/0000-0002-7455-5434","https://orcid.org/0000-0002-1631-8326"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Belhadj Karim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9965999722480774,"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":0.9965999722480774,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.000699999975040555,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.00039999998989515007,"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/nodal-domains","display_name":"nodal domains","score":0.9620000123977661},{"id":"https://openalex.org/keywords/p-laplacian","display_name":"p-Laplacian","score":0.996999979019165},{"id":"https://openalex.org/keywords/eigenvalue-problem","display_name":"eigenvalue problem","score":0.8080000281333923},{"id":"https://openalex.org/keywords/eigenvalue-multiplicity","display_name":"eigenvalue multiplicity","score":0.734000027179718},{"id":"https://openalex.org/keywords/dirichlet-boundary-conditions","display_name":"Dirichlet boundary conditions","score":0.5659999847412109},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.5450000166893005},{"id":"https://openalex.org/keywords/nonlinear-elliptic-operators","display_name":"nonlinear elliptic operators","score":0.5329999923706055}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7152047157287598},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.703665018081665},{"id":"https://openalex.org/C83330619","wikidata":"https://www.wikidata.org/wiki/Q21124872","display_name":"NODAL","level":2,"score":0.6801114082336426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6605789661407471},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6455941796302795},{"id":"https://openalex.org/C203269682","wikidata":"https://www.wikidata.org/wiki/Q7116898","display_name":"p-Laplacian","level":3,"score":0.626533031463623},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5953719615936279},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5470959544181824},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47297847270965576},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4300234615802765},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21801412105560303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1738920509815216},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0805489718914032},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.06336411833763123},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.043397098779678345},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.649.8125","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.649.8125","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://campus.mst.edu/adsa/contents/v2n2p1.pdf","raw_type":"text"},{"id":"mag:2162144866","doi":null,"is_oa":false,"landing_page_url":"http://campus.mst.edu/adsa/contents/v2n2p1.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1230513566","https://openalex.org/W1502485581","https://openalex.org/W1981482176","https://openalex.org/W2058065296","https://openalex.org/W2104996923","https://openalex.org/W2591883940"],"related_works":["https://openalex.org/W2058065296","https://openalex.org/W2047450154","https://openalex.org/W2338550860","https://openalex.org/W7166816913","https://openalex.org/W1808587840","https://openalex.org/W7095432643","https://openalex.org/W7167496292","https://openalex.org/W6991534431","https://openalex.org/W2548744876"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"the":[5,22,53],"eigenvalue":[6,56],"problem":[7],"\u2212pu":[8],"=":[9],"\u03bb(m)|u|p\u22122u,":[10],"u":[11],"\u2208":[12],"W":[13],"1,p":[14],"0":[15],"()":[16],"where":[17],"p>":[18],"1,":[19],"p":[20,47],"is":[21,27,37],"p-Laplacian":[23],"operator,":[24],"\u03bb>":[25],"0,":[26],"a":[28,38],"bounded":[29],"domain":[30],"in":[31,42],"RN(N":[32],"\u2265":[33],"1)":[34],"and":[35,48],"m":[36],"given":[39],"positive":[40,55],"function":[41],"Lr()":[43],"(r":[44],"depending":[45],"on":[46],"N).":[49],"We":[50],"prove":[51],"that":[52],"second":[54],"admits":[57],"exactly":[58],"two":[59],"nodal":[60],"domains.":[61]},"counts_by_year":[{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}
