{"id":"https://openalex.org/W147689634","doi":null,"title":"Half-linear dynamic equations on time scales: IVP and oscillatory properties","display_name":"Half-linear dynamic equations on time scales: IVP and oscillatory properties","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W147689634","mag":"147689634"},"language":"en","primary_location":{"id":"mag:147689634","doi":null,"is_oa":false,"landing_page_url":"https://is.muni.cz/publication/487585/cs","pdf_url":null,"source":{"id":"https://openalex.org/S2764636513","display_name":"Nonlinear functional analysis and applications","issn_l":"1229-1595","issn":["1229-1595","2466-0973"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","kci-registered","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Nonlinear functional analysis and applications","raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090625750","display_name":"Pavel \u0158eh\u00e1k","orcid":"https://orcid.org/0000-0002-2452-2204","observed_orcids":["https://orcid.org/0000-0002-2452-2204","https://orcid.org/0009-0005-4128-7698"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P. \u0158eh\u00e1k","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2452-2204","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5090625750"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7161,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.92762135,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"7","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":9.999999747378752e-05,"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"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/half-linear-dynamic-equations","display_name":"half-linear dynamic equations","score":0.9950000047683716},{"id":"https://openalex.org/keywords/timescales","display_name":"time scales","score":0.972000002861023},{"id":"https://openalex.org/keywords/oscillation-theory","display_name":"oscillation theory","score":0.9509999752044678},{"id":"https://openalex.org/keywords/sturm-liouville-equation","display_name":"Sturm-Liouville equation","score":0.8429999947547913},{"id":"https://openalex.org/keywords/riccati-technique","display_name":"Riccati technique","score":0.9700000286102295},{"id":"https://openalex.org/keywords/variational-principle","display_name":"variational principle","score":0.9900000095367432},{"id":"https://openalex.org/keywords/sturmian-theory","display_name":"Sturmian theory","score":0.9610000252723694},{"id":"https://openalex.org/keywords/nonoscillation-criteria","display_name":"nonoscillation criteria","score":0.8799999952316284},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"initial value problems","score":0.8050000071525574},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.9760000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7920528650283813},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7890800833702087},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.651075005531311},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5508013367652893},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5249788165092468},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5149543881416321},{"id":"https://openalex.org/C190233882","wikidata":"https://www.wikidata.org/wiki/Q289610","display_name":"Oscillation theory","level":5,"score":0.4888560175895691},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.4807184040546417},{"id":"https://openalex.org/C2989370511","wikidata":"https://www.wikidata.org/wiki/Q18381590","display_name":"Dynamic equation","level":3,"score":0.45229068398475647},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.441193550825119},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.41719335317611694},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3688545227050781},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1925291121006012},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19073989987373352},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.09792658686637878},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08150577545166016},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:147689634","doi":null,"is_oa":false,"landing_page_url":"https://is.muni.cz/publication/487585/cs","pdf_url":null,"source":{"id":"https://openalex.org/S2764636513","display_name":"Nonlinear functional analysis and applications","issn_l":"1229-1595","issn":["1229-1595","2466-0973"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","kci-registered","norway-1","poland-20","russia-white-list-3"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Nonlinear functional analysis and applications","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2595151183","https://openalex.org/W2437751825","https://openalex.org/W7095422891","https://openalex.org/W2073680172","https://openalex.org/W2100959236","https://openalex.org/W2605202061","https://openalex.org/W4287006939","https://openalex.org/W2057321111","https://openalex.org/W3136479425","https://openalex.org/W2910755613"],"abstract_inverted_index":{"In":[0,43],"this":[1,69],"paper":[2],"we":[3,81],"show":[4],"how":[5],"the":[6,13,25,45,48,63,72,94],"basic":[7],"results":[8],"of":[9,12,47,65,68,98,101],"oscillation":[10,85],"theory":[11],"Sturm--Liouville":[14],"linear":[15],"differential":[16],"equation":[17,28,56],"$$":[18,20,29,32],"(r(t)y')'+p(t)y=0":[19],"can":[21],"be":[22],"extended":[23],"to":[24],"half-linear":[26],"dynamic":[27],"(r(t)\\Phi(y^\\Delta))^\\Delta+p(t)\\Phi(y^\\sigma)=0":[30],"\\tag{HL$^\\Delta$E}":[31],"on":[33],"an":[34,79],"arbitrary":[35],"time":[36],"scale,":[37],"where":[38],"$\\Phi(x)=|x|^{\\alpha-1}\\sgn":[39],"x$":[40],"with":[41],"$\\alpha>1$.":[42],"particular,":[44],"generalization":[46],"so":[49],"called":[50],"Roundabout":[51],"theorem":[52],"is":[53],"proved":[54],"for":[55,62,89],"(HL$^\\triangle$E),":[57],"which":[58],"provides":[59],"powerful":[60],"tools":[61],"investigation":[64],"oscillatory":[66],"properties":[67],"equation,":[70],"namely":[71],"Riccati":[73],"technique":[74],"and":[75,86,96],"variational":[76],"principle.":[77],"As":[78],"application":[80],"present":[82],"Sturmian":[83],"theory,":[84],"nonoscillation":[87],"criteria":[88],"(HL$^\\Delta$E).":[90],"The":[91],"questions":[92],"concerning":[93],"existence":[95],"uniqueness":[97],"a":[99],"solution":[100],"initial":[102],"value":[103],"problem":[104],"are":[105],"also":[106],"discussed.":[107]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-09-24T07:57:37.273135","created_date":"2016-06-24T00:00:00"}
