{"id":"https://openalex.org/W4402283698","doi":"https://doi.org/10.3390/sym16091156","title":"Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations","display_name":"Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations","publication_year":2024,"publication_date":"2024-09-05","ids":{"openalex":"https://openalex.org/W4402283698","doi":"https://doi.org/10.3390/sym16091156"},"language":"en","primary_location":{"id":"doi:10.3390/sym16091156","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16091156","pdf_url":"https://www.mdpi.com/2073-8994/16/9/1156/pdf?version=1725533364","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/9/1156/pdf?version=1725533364","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021878148","display_name":"Taher S. Hassan","orcid":"https://orcid.org/0000-0003-2907-3353"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]},{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["EG","IT","SA"],"is_corresponding":true,"raw_author_name":"Taher S. Hassan","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia","Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2907-3353","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075452466","display_name":"Loredana Florentina Iambor","orcid":"https://orcid.org/0000-0001-8845-3095"},"institutions":[{"id":"https://openalex.org/I162871001","display_name":"University of Oradea","ror":"https://ror.org/00wzhv093","country_code":"RO","type":"education","lineage":["https://openalex.org/I162871001"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Loredana Florentina Iambor","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania"],"raw_orcid":"https://orcid.org/0000-0001-8845-3095","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania","institution_ids":["https://openalex.org/I162871001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016978313","display_name":"Sorin Mure\u015fan","orcid":"https://orcid.org/0000-0002-1882-3748"},"institutions":[{"id":"https://openalex.org/I162871001","display_name":"University of Oradea","ror":"https://ror.org/00wzhv093","country_code":"RO","type":"education","lineage":["https://openalex.org/I162871001"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Sorin Mure\u015fan","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania","institution_ids":["https://openalex.org/I162871001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111317136","display_name":"Khalid Alenzi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khalid Alenzi","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083599578","display_name":"Ismoil Odinaev","orcid":"https://orcid.org/0000-0003-2434-1929"},"institutions":[{"id":"https://openalex.org/I130823665","display_name":"Ural Federal University","ror":"https://ror.org/00hs7dr46","country_code":"RU","type":"education","lineage":["https://openalex.org/I130823665"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Ismoil Odinaev","raw_affiliation_strings":["Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia"],"raw_orcid":"https://orcid.org/0000-0003-2434-1929","affiliations":[{"raw_affiliation_string":"Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia","institution_ids":["https://openalex.org/I130823665"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081682745","display_name":"Khudhayr A. Rashedi","orcid":"https://orcid.org/0000-0003-1409-1794"},"institutions":[{"id":"https://openalex.org/I4210088963","display_name":"University of Ha'il","ror":"https://ror.org/013w98a82","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210088963"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khudhayr A. Rashedi","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia","institution_ids":["https://openalex.org/I4210088963"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5021878148","https://openalex.org/A5075452466"],"corresponding_institution_ids":["https://openalex.org/I159247623","https://openalex.org/I162871001","https://openalex.org/I4210088963","https://openalex.org/I4210155399"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24300813,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"9","first_page":"1156","last_page":"1156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/dynamic-equation","display_name":"Dynamic equation","score":0.8921220302581787},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.6997994184494019},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.585208535194397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.533629834651947},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5022966861724854},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.4918072521686554},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.45159339904785156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44404393434524536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38197845220565796},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3479465842247009},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28880900144577026},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.24197712540626526},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1902385950088501},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.18666759133338928},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10087567567825317},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05322086811065674}],"concepts":[{"id":"https://openalex.org/C2989370511","wikidata":"https://www.wikidata.org/wiki/Q18381590","display_name":"Dynamic equation","level":3,"score":0.8921220302581787},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.6997994184494019},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.585208535194397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.533629834651947},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5022966861724854},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.4918072521686554},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.45159339904785156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44404393434524536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38197845220565796},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3479465842247009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28880900144577026},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.24197712540626526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1902385950088501},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.18666759133338928},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10087567567825317},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05322086811065674},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym16091156","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16091156","pdf_url":"https://www.mdpi.com/2073-8994/16/9/1156/pdf?version=1725533364","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:elar.urfu.ru:10995/143964","is_oa":true,"landing_page_url":"https://www.mdpi.com/2073-8994/16/9/1156/pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4406922546","display_name":"Electronic Archive of Ural Federal University (ELAR UrFU)","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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:ba090eed2808451495c8a7b2a03c9f95","is_oa":false,"landing_page_url":"https://doaj.org/article/ba090eed2808451495c8a7b2a03c9f95","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":"Symmetry, Vol 16, Iss 9, p 1156 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16091156","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16091156","pdf_url":"https://www.mdpi.com/2073-8994/16/9/1156/pdf?version=1725533364","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402283698.pdf","grobid_xml":"https://content.openalex.org/works/W4402283698.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W182939265","https://openalex.org/W271810198","https://openalex.org/W1522419168","https://openalex.org/W1978603909","https://openalex.org/W1994955329","https://openalex.org/W2001401829","https://openalex.org/W2009704386","https://openalex.org/W2018570027","https://openalex.org/W2037930075","https://openalex.org/W2066397800","https://openalex.org/W2137369682","https://openalex.org/W2154081959","https://openalex.org/W2514711739","https://openalex.org/W2766862070","https://openalex.org/W2804035762","https://openalex.org/W2898746352","https://openalex.org/W2902273760","https://openalex.org/W2902943087","https://openalex.org/W3030742673","https://openalex.org/W3045836994","https://openalex.org/W3101681039","https://openalex.org/W3167176117","https://openalex.org/W3170331393","https://openalex.org/W3188689648","https://openalex.org/W3189949196","https://openalex.org/W3192319191","https://openalex.org/W3207374618","https://openalex.org/W4213115141","https://openalex.org/W4240644230","https://openalex.org/W4241048020","https://openalex.org/W4311253152","https://openalex.org/W4388215494","https://openalex.org/W6607385462","https://openalex.org/W6725877007","https://openalex.org/W6755442544","https://openalex.org/W6757023948","https://openalex.org/W6776706214","https://openalex.org/W6809105228"],"related_works":["https://openalex.org/W2057030324","https://openalex.org/W1968731853","https://openalex.org/W2137980878","https://openalex.org/W2151813854","https://openalex.org/W2018954023","https://openalex.org/W2142669796","https://openalex.org/W2900582606","https://openalex.org/W3148257963","https://openalex.org/W2740452798","https://openalex.org/W2394006932"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"second-order":[3,38],"functional":[4],"dynamic":[5,39,51,73],"equations":[6],"with":[7],"mixed":[8],"nonlinearities":[9],"on":[10,50],"an":[11,77],"arbitrary":[12],"unbounded":[13],"above-time":[14],"scale,":[15],"T.":[16],"We":[17,75],"will":[18],"use":[19],"a":[20,44],"unified":[21],"time":[22],"scale":[23],"approach":[24],"and":[25,57],"the":[26,35,48,61,67,81],"well-known":[27],"Riccati":[28],"technique":[29],"to":[30,72,79],"derive":[31],"oscillation":[32],"criteria":[33],"of":[34,64,70,83],"Nehari-type":[36],"for":[37,66],"equations.":[40,52,74],"The":[41,53],"findings":[42],"demonstrate":[43,80],"significant":[45],"improvement":[46],"in":[47,59],"literature":[49],"symmetry":[54],"is":[55],"beneficial":[56],"influential":[58],"defining":[60],"right":[62],"style":[63],"study":[65],"qualitative":[68],"behavior":[69],"solutions":[71],"include":[76],"example":[78],"significance":[82],"our":[84],"results.":[85]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}