{"id":"https://openalex.org/W4283748526","doi":"https://doi.org/10.1155/2022/3407776","title":"Modified Oscillation Results for Advanced Difference Equations of Second-Order","display_name":"Modified Oscillation Results for Advanced Difference Equations of Second-Order","publication_year":2022,"publication_date":"2022-06-30","ids":{"openalex":"https://openalex.org/W4283748526","doi":"https://doi.org/10.1155/2022/3407776"},"language":"en","primary_location":{"id":"doi:10.1155/2022/3407776","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/3407776","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/3407776.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2022/3407776.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014915773","display_name":"George E. Chatzarakis","orcid":"https://orcid.org/0000-0002-0477-1895"},"institutions":[{"id":"https://openalex.org/I254421610","display_name":"School of Pedagogical and Technological Education","ror":"https://ror.org/04v3r9z94","country_code":"GR","type":"education","lineage":["https://openalex.org/I254421610"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"G. E. Chatzarakis","raw_affiliation_strings":["Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, Marousi, 15122 Athens, Greece"],"raw_orcid":"https://orcid.org/0000-0002-0477-1895","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, Marousi, 15122 Athens, Greece","institution_ids":["https://openalex.org/I254421610"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057292177","display_name":"N. Indrajith","orcid":null},"institutions":[{"id":"https://openalex.org/I157674215","display_name":"Presidency University","ror":"https://ror.org/04xgbph11","country_code":"IN","type":"education","lineage":["https://openalex.org/I157674215"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"N. Indrajith","raw_affiliation_strings":["Department of Mathematics, Presidency College, Chennai 600005, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Presidency College, Chennai 600005, India","institution_ids":["https://openalex.org/I157674215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069795166","display_name":"S. L. Panetsos","orcid":"https://orcid.org/0000-0002-4517-0922"},"institutions":[{"id":"https://openalex.org/I254421610","display_name":"School of Pedagogical and Technological Education","ror":"https://ror.org/04v3r9z94","country_code":"GR","type":"education","lineage":["https://openalex.org/I254421610"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"S. L. Panetsos","raw_affiliation_strings":["Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, Marousi, 15122 Athens, Greece"],"raw_orcid":"https://orcid.org/0000-0002-4517-0922","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, Marousi, 15122 Athens, Greece","institution_ids":["https://openalex.org/I254421610"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091738538","display_name":"E. Thandapani","orcid":null},"institutions":[{"id":"https://openalex.org/I215927","display_name":"University of Madras","ror":"https://ror.org/04jmt9361","country_code":"IN","type":"education","lineage":["https://openalex.org/I215927"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"E. Thandapani","raw_affiliation_strings":["Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India"],"raw_orcid":"https://orcid.org/0000-0001-6801-4191","affiliations":[{"raw_affiliation_string":"Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India","institution_ids":["https://openalex.org/I215927"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069795166"],"corresponding_institution_ids":["https://openalex.org/I254421610"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.343,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45701044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2022","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9995999932289124,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9909999966621399,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/physics","display_name":"Physics","score":0.41622674465179443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3705025017261505}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41622674465179443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3705025017261505}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/3407776","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/3407776","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/3407776.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnljam:3407776","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2022/3407776.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:4710df03b27a4cf3adc2a126a85abf28","is_oa":true,"landing_page_url":"https://doaj.org/article/4710df03b27a4cf3adc2a126a85abf28","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/3407776","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/3407776","pdf_url":"https://downloads.hindawi.com/journals/jam/2022/3407776.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283748526.pdf","grobid_xml":"https://content.openalex.org/works/W4283748526.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W13811575","https://openalex.org/W639417630","https://openalex.org/W2016342440","https://openalex.org/W2030007865","https://openalex.org/W2057565557","https://openalex.org/W2137980878","https://openalex.org/W2766862070","https://openalex.org/W2802347107","https://openalex.org/W2804035762","https://openalex.org/W2953446726","https://openalex.org/W2998602493","https://openalex.org/W3006981577","https://openalex.org/W3012487426","https://openalex.org/W3019276055","https://openalex.org/W3101681039","https://openalex.org/W3170331393","https://openalex.org/W3211862163","https://openalex.org/W4207025955","https://openalex.org/W4220883094"],"related_works":["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/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5],"new":[6,134],"method":[7],"to":[8,143],"establish":[9],"the":[10,18,76,137,145],"oscillation":[11],"of":[12,17],"advanced":[13],"second-order":[14],"difference":[15,78],"equations":[16],"form":[19],"<math":[20,80],"xmlns=\"http://www.w3.org/1998/Math/MathML\"":[21,81],"id=\"M1\">":[22],"<mi>\u0394</mi>":[23,36,83,96],"<mfenced":[24,29,38,49,57,62,84,89,98,109,117],"open=\"(\"":[25,30,39,50,58,63,85,90,99,110,118],"close=\")\">":[26,31,40,51,59,64,86,91,100,111,119],"<mrow>":[27,32,41,52,60,65,87,92,101,112,120],"<mi>\u03b7</mi>":[28,88],"<mi>\u2113</mi>":[33,42,53,66,93,102,113,121],"</mrow>":[34,43,45,54,67,69,94,103,105,114,124],"</mfenced>":[35,44,46,55,68,70,95,104,106,115,125],"<mi>\u03c5</mi>":[37,56,97,116],"<mo>+</mo>":[47,107,122],"<mi>\u03c1</mi>":[48],"<mi>\u03c3</mi>":[61],"<mo>=</mo>":[71,126],"<mn>0</mn>":[72,127],"<mo>,</mo>":[73],"</math>":[74,129],"using":[75],"ordinary":[77],"equation":[79],"id=\"M2\">":[82],"<mi>q</mi>":[108],"<mn>1</mn>":[123],"<mo>.</mo>":[128],"The":[130],"obtained":[131],"results":[132],"are":[133],"and":[135],"improve":[136],"existing":[138],"criteria.":[139],"We":[140],"provide":[141],"examples":[142],"illustrate":[144],"main":[146],"results.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}