{"id":"https://openalex.org/W4386304026","doi":"https://doi.org/10.3390/axioms12090841","title":"New Results for the Investigation of the Asymptotic Behavior of Solutions of Nonlinear Perturbed Differential Equations","display_name":"New Results for the Investigation of the Asymptotic Behavior of Solutions of Nonlinear Perturbed Differential Equations","publication_year":2023,"publication_date":"2023-08-30","ids":{"openalex":"https://openalex.org/W4386304026","doi":"https://doi.org/10.3390/axioms12090841"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12090841","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090841","pdf_url":"https://www.mdpi.com/2075-1680/12/9/841/pdf?version=1693362213","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/9/841/pdf?version=1693362213","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074973583","display_name":"Osama Moaaz","orcid":"https://orcid.org/0000-0003-3850-1022"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]},{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"Osama Moaaz","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia","Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073214349","display_name":"Wedad Albalawi","orcid":"https://orcid.org/0000-0002-9667-3933"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Wedad Albalawi","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073214349","https://openalex.org/A5074973583"],"corresponding_institution_ids":["https://openalex.org/I106778892","https://openalex.org/I156216236","https://openalex.org/I159247623"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17559217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"9","first_page":"841","last_page":"841"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9955999851226807,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9828000068664551,"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/riccati-equation","display_name":"Riccati equation","score":0.7311100959777832},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6166337728500366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6038127541542053},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.580394983291626},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5694575309753418},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5429638624191284},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.5133609175682068},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5063425302505493},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4801637530326843},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3648635447025299},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2637988328933716},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1259591281414032}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.7311100959777832},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6166337728500366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6038127541542053},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.580394983291626},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5694575309753418},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5429638624191284},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.5133609175682068},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5063425302505493},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4801637530326843},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3648635447025299},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2637988328933716},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1259591281414032},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12090841","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090841","pdf_url":"https://www.mdpi.com/2075-1680/12/9/841/pdf?version=1693362213","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:bac114d5302a4a8d9481b2d2a8778d35","is_oa":true,"landing_page_url":"https://doaj.org/article/bac114d5302a4a8d9481b2d2a8778d35","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 9, p 841 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/9/841/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12090841","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12090841","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090841","pdf_url":"https://www.mdpi.com/2075-1680/12/9/841/pdf?version=1693362213","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386304026.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W19721600","https://openalex.org/W607066590","https://openalex.org/W1550383043","https://openalex.org/W1916089472","https://openalex.org/W1964240948","https://openalex.org/W1977136522","https://openalex.org/W1992110793","https://openalex.org/W1994975281","https://openalex.org/W1998364710","https://openalex.org/W2004099014","https://openalex.org/W2009704386","https://openalex.org/W2046944180","https://openalex.org/W2051926255","https://openalex.org/W2055067428","https://openalex.org/W2092886073","https://openalex.org/W2113754706","https://openalex.org/W2165076427","https://openalex.org/W2188565877","https://openalex.org/W2367894112","https://openalex.org/W2751107753","https://openalex.org/W2884070321","https://openalex.org/W2891155438","https://openalex.org/W3046212638","https://openalex.org/W3112436622","https://openalex.org/W3135392168","https://openalex.org/W3183700507","https://openalex.org/W3184485343","https://openalex.org/W3185184312","https://openalex.org/W3187585064","https://openalex.org/W3203005175","https://openalex.org/W4311185912","https://openalex.org/W4312631086","https://openalex.org/W4319865347","https://openalex.org/W4320151948","https://openalex.org/W4388215494","https://openalex.org/W6683867241","https://openalex.org/W6687327942","https://openalex.org/W6787403862","https://openalex.org/W6791745212","https://openalex.org/W6848818980","https://openalex.org/W6848963452"],"related_works":["https://openalex.org/W2123585262","https://openalex.org/W2937301577","https://openalex.org/W3081931655","https://openalex.org/W2062635734","https://openalex.org/W2072100489","https://openalex.org/W3176473605","https://openalex.org/W3160917256","https://openalex.org/W1755828065","https://openalex.org/W3158420315","https://openalex.org/W2367945514"],"abstract_inverted_index":{"This":[0],"study":[1,39],"focuses":[2],"on":[3],"investigating":[4],"the":[5,17,30,36,53,56,63,71,93,111],"oscillatory":[6,44],"properties":[7],"of":[8,12,32,55,92,101,110,114,122],"a":[9,49],"particular":[10],"class":[11],"perturbed":[13],"differential":[14],"equations":[15],"in":[16,62,105],"noncanonical":[18],"case.":[19,65],"Our":[20],"research":[21],"aims":[22],"to":[23,35,78,89],"establish":[24],"more":[25],"effective":[26],"criteria":[27],"for":[28],"evaluating":[29],"absence":[31],"positive":[33],"solutions":[34],"equation":[37,58,61],"under":[38],"and":[40,108],"subsequently":[41],"investigate":[42],"its":[43,106],"behavior.":[45],"We":[46],"also":[47],"perform":[48],"comparative":[50],"analysis,":[51],"contrasting":[52],"oscillation":[54],"studied":[57],"with":[59,75],"another":[60],"canonical":[64],"To":[66],"achieve":[67],"this,":[68],"we":[69,84],"employ":[70],"Riccati":[72],"technique":[73],"along":[74],"other":[76],"methods":[77],"obtain":[79],"several":[80],"sufficient":[81],"criteria.":[82],"Furthermore,":[83],"apply":[85],"these":[86],"new":[87],"conditions":[88],"specific":[90],"instances":[91],"considered":[94],"equation,":[95],"assessing":[96],"their":[97],"performance.":[98],"The":[99],"significance":[100],"our":[102],"work":[103],"lies":[104],"extension":[107],"broadening":[109],"existing":[112],"body":[113],"literature,":[115],"contributing":[116],"novel":[117],"insights":[118],"into":[119],"this":[120],"field":[121],"study.":[123]},"counts_by_year":[],"updated_date":"2026-02-03T00:53:05.648605","created_date":"2025-10-10T00:00:00"}
