{"id":"https://openalex.org/W4294676071","doi":"https://doi.org/10.1007/s10998-022-00479-1","title":"Oscillation results via comparison theorems for fourth-order delay three-terms difference equations","display_name":"Oscillation results via comparison theorems for fourth-order delay three-terms difference equations","publication_year":2022,"publication_date":"2022-09-06","ids":{"openalex":"https://openalex.org/W4294676071","doi":"https://doi.org/10.1007/s10998-022-00479-1"},"language":"lv","primary_location":{"id":"doi:10.1007/s10998-022-00479-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10998-022-00479-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-022-00479-1.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10998-022-00479-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054769322","display_name":"Ma\u0142gorzata Migda","orcid":"https://orcid.org/0000-0003-3188-1173"},"institutions":[{"id":"https://openalex.org/I46597724","display_name":"Pozna\u0144 University of Technology","ror":"https://ror.org/00p7p3302","country_code":"PL","type":"education","lineage":["https://openalex.org/I46597724"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Ma\u0142gorzata Migda","raw_affiliation_strings":["Poznan University of Technology, Piotrowo 3A, 60-965, Pozna\u0144, Poland","Poznan University of Technology, Pozna\u0144, Poland"],"raw_orcid":"https://orcid.org/0000-0003-3188-1173","affiliations":[{"raw_affiliation_string":"Poznan University of Technology, Piotrowo 3A, 60-965, Pozna\u0144, Poland","institution_ids":["https://openalex.org/I46597724"]},{"raw_affiliation_string":"Poznan University of Technology, Pozna\u0144, Poland","institution_ids":["https://openalex.org/I46597724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073212928","display_name":"Ewa Schmeidel","orcid":"https://orcid.org/0000-0001-8893-2205"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Ewa Schmeidel","raw_affiliation_strings":["Institute of Computer Science, University of Bialystok, Ciolkowskiego 1M, 15-245, Bialystok, Poland","Institute of Computer Science, University of Bialystok, Bialystok, Poland"],"raw_orcid":"https://orcid.org/0000-0001-8893-2205","affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Bialystok, Ciolkowskiego 1M, 15-245, Bialystok, Poland","institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"]},{"raw_affiliation_string":"Institute of Computer Science, University of Bialystok, Bialystok, Poland","institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032992722","display_name":"Ma\u0142gorzata Zdanowicz","orcid":"https://orcid.org/0000-0001-6951-5721"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Ma\u0142gorzata Zdanowicz","raw_affiliation_strings":["Institute of Computer Science, University of Bialystok, Ciolkowskiego 1M, 15-245, Bialystok, Poland","Institute of Computer Science, University of Bialystok, Bialystok, Poland"],"raw_orcid":"https://orcid.org/0000-0001-6951-5721","affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Bialystok, Ciolkowskiego 1M, 15-245, Bialystok, Poland","institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"]},{"raw_affiliation_string":"Institute of Computer Science, University of Bialystok, Bialystok, Poland","institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037140560","display_name":"Janusz Migda","orcid":"https://orcid.org/0000-0002-0855-6180"},"institutions":[{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Janusz Migda","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614, Pozna\u0144, Poland","Faculty of Mathematics and Computer Science, A. Mickiewicz University, Pozna\u0144, Poland"],"raw_orcid":"https://orcid.org/0000-0002-0855-6180","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614, Pozna\u0144, Poland","institution_ids":["https://openalex.org/I59411706"]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, A. Mickiewicz University, Pozna\u0144, Poland","institution_ids":["https://openalex.org/I59411706"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5032992722"],"corresponding_institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13449127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"86","issue":"2","first_page":"395","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9987000226974487,"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":0.9987000226974487,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9772999882698059,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9452999830245972,"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/algorithm","display_name":"Algorithm","score":0.4708615839481354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2099623680114746}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4708615839481354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2099623680114746}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10998-022-00479-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10998-022-00479-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-022-00479-1.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10998-022-00479-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10998-022-00479-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10998-022-00479-1.pdf","source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4294676071.pdf","grobid_xml":"https://content.openalex.org/works/W4294676071.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W13811575","https://openalex.org/W639417630","https://openalex.org/W1985110853","https://openalex.org/W1992523338","https://openalex.org/W2008575940","https://openalex.org/W2016501748","https://openalex.org/W2017645034","https://openalex.org/W2030038636","https://openalex.org/W2050534668","https://openalex.org/W2078997962","https://openalex.org/W2104162382","https://openalex.org/W2124023730","https://openalex.org/W2140468114","https://openalex.org/W2153424360","https://openalex.org/W2155055617","https://openalex.org/W2561963369","https://openalex.org/W2620810305","https://openalex.org/W2738610876","https://openalex.org/W2800363432","https://openalex.org/W2946402511","https://openalex.org/W3036371786","https://openalex.org/W4388215494"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4],"establish":[5],"sufficient":[6],"conditions":[7],"for":[8],"the":[9,50],"oscillation":[10],"of":[11,14],"all":[12],"solutions":[13],"equation":[15],"$$\\begin{aligned}":[16],"\\varDelta":[17],"^4x(n)+p(n)\\varDelta":[18],"x(n+1)+q(n)x(n-\\tau":[19],")=0":[20],"\\end{aligned}$$":[21],"<mml:math":[22],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:msup><mml:mi>\u0394</mml:mi><mml:mn>4</mml:mn></mml:msup><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>p</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>\u0394</mml:mi><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>q</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>\u03c4</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math>":[23],"via":[24],"comparison":[25],"with":[26],"some":[27],"first":[28],"order":[29],"delay":[30],"difference":[31],"equations":[32],"whose":[33],"oscillatory":[34],"characters":[35],"are":[36,45],"known.":[37],"The":[38],"presented":[39],"criterion":[40],"is":[41],"easily":[42],"verifiable.":[43],"Examples":[44],"also":[46],"given":[47],"to":[48],"illustrate":[49],"main":[51],"result.":[52]},"counts_by_year":[],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}