{"id":"https://openalex.org/W4410872364","doi":"https://doi.org/10.3934/nhm.2025025","title":"An integral system of Matukuma type with negative exponents","display_name":"An integral system of Matukuma type with negative exponents","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4410872364","doi":"https://doi.org/10.3934/nhm.2025025"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2025025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2025025","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2025025","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049260993","display_name":"Changhong Li","orcid":null},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Changhong Li","raw_affiliation_strings":["School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049260993"],"corresponding_institution_ids":["https://openalex.org/I100930933"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1649451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"2","first_page":"566","last_page":"589"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9993000030517578,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9993000030517578,"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/T13234","display_name":"advanced mathematical theories","score":0.9980999827384949,"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":0.9975000023841858,"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/type","display_name":"Type (biology)","score":0.5982021689414978},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4679965376853943},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44825834035873413},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38146886229515076},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.0970926582813263}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5982021689414978},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4679965376853943},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44825834035873413},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38146886229515076},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0970926582813263},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2025025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2025025","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ed0cbc2d0250494c8b6e5ef9038f0bdc","is_oa":false,"landing_page_url":"https://doaj.org/article/ed0cbc2d0250494c8b6e5ef9038f0bdc","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 20, Iss 2, Pp 566-589 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2025025","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2025025","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W2004755906","https://openalex.org/W2011667189","https://openalex.org/W2027060021","https://openalex.org/W2046485610","https://openalex.org/W2078234954","https://openalex.org/W2081300880","https://openalex.org/W2088264197","https://openalex.org/W2095581407","https://openalex.org/W2137190043","https://openalex.org/W2144078706","https://openalex.org/W2315919721","https://openalex.org/W2341223996","https://openalex.org/W2463912507","https://openalex.org/W2537314035","https://openalex.org/W2811278105","https://openalex.org/W2969203746","https://openalex.org/W2989927668","https://openalex.org/W3025096263","https://openalex.org/W3101243313","https://openalex.org/W4281609114","https://openalex.org/W4294613007","https://openalex.org/W4304688258","https://openalex.org/W4386772866","https://openalex.org/W4387835652","https://openalex.org/W4404612929","https://openalex.org/W4407418314"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W2271181815"],"abstract_inverted_index":{"We":[0,89,116],"study":[1],"positive":[2,97],"solutions":[3,98,125],"to":[4,99,105],"the":[5,91,100,119,127],"integral":[6],"system$":[7],"\\begin{cases}":[8],"u(x)":[9],"=":[10,23],"\\int\\limits_{":[11,24],"\\mathbb":[12,19,25,32,52,70],"R^N}\\frac{K(y)v^{-p}(y)}{":[13],"|x-y|^{N-\\alpha}}":[14],"dy\\quad\\text{":[15,28],"for":[16,29,73],"all":[17,30],"}x\\in":[18,31],"R^N,":[20,33],"\\\\":[21],"v(x)":[22],"R^N}\\frac{L(y)u^{-q}(y)}{":[26],"|x-y|^{N-\\beta}}":[27],"\\end{cases}":[34],"$where":[35],"$":[36,42,47,49,56,62,67,69,75,79,82,106,111,113],"p,":[37,109],"q":[38],">":[39,77,84,86],"0":[40,78,87],"$,":[41,72],"\\alpha,":[43,107],"\\beta\\in":[44],"(0,":[45,54],"N)":[46],"and":[48,80,94,112,121],"K,":[50],"L:":[51],"R^N\\to":[53],"\\infty)":[55],"are":[57],"continuous":[58],"functions":[59],"which":[60],"satisfy":[61],"C_1(1+|x|)^{-\\gamma}\\leq":[63],"K(x),":[64],"L(x)\\leq":[65],"C_2(1+|x|)^{-\\gamma}":[66],"in":[68],"R^N":[71],"some":[74],"\\gamma":[76,114],"constants":[81],"C_2":[83],"C_1":[85],"$.":[88,115],"discuss":[90],"existence,":[92],"nonexistence,":[93],"uniqueness":[95],"of":[96,126],"above":[101],"system":[102],"with":[103],"respect":[104],"\\beta,":[108],"q,":[110],"also":[117],"classify":[118],"finite":[120],"infinite":[122],"total":[123],"mass":[124],"system.":[128]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
