{"title":"满足Dirichlet边界条件的非线性ν阶Atıcı-Eloe分数阶差分方程的非平凡解","authors":"J. Henderson","doi":"10.7153/dea-2022-14-08","DOIUrl":null,"url":null,"abstract":". For 1 < ν (cid:2) 2 a real number and T (cid:3) 2 a natural number, by an application of a Krasnosel’skii-Zabreiko fi xed point theorem, nontrivial solutions are established for a nonlinear ν th order At ı c ı -Eloe fractional difference equation, Δ ν u ( t )+ f ( u ( t + ν − 1 )) = 0, t ∈ { 1 , 2 ,..., T + 1 } , satisfying the Dirichlet boundary conditions u ( ν − 2 ) = u ( ν + T + 1 ) = 0 ,","PeriodicalId":179999,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Nontrivial solutions for a nonlinear νth order Atıcı-Eloe fractional difference equation satisfying Dirichlet boundary conditions\",\"authors\":\"J. Henderson\",\"doi\":\"10.7153/dea-2022-14-08\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". For 1 < ν (cid:2) 2 a real number and T (cid:3) 2 a natural number, by an application of a Krasnosel’skii-Zabreiko fi xed point theorem, nontrivial solutions are established for a nonlinear ν th order At ı c ı -Eloe fractional difference equation, Δ ν u ( t )+ f ( u ( t + ν − 1 )) = 0, t ∈ { 1 , 2 ,..., T + 1 } , satisfying the Dirichlet boundary conditions u ( ν − 2 ) = u ( ν + T + 1 ) = 0 ,\",\"PeriodicalId\":179999,\"journal\":{\"name\":\"Differential Equations & Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/dea-2022-14-08\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2022-14-08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
. 对于1 < ν (cid:2) 2为实数,T (cid:3) 2为自然数,应用Krasnosel 'skii-Zabreiko不动点定理,建立了一类非线性ν五阶At -Eloe分数阶差分方程的非平凡解,Δ ν u (T)+ f (u (T + ν−1))= 0,T∈{1,2,…, T + 1},满足Dirichlet边界条件u (ν−2)= u (ν + T + 1) = 0,
Nontrivial solutions for a nonlinear νth order Atıcı-Eloe fractional difference equation satisfying Dirichlet boundary conditions
. For 1 < ν (cid:2) 2 a real number and T (cid:3) 2 a natural number, by an application of a Krasnosel’skii-Zabreiko fi xed point theorem, nontrivial solutions are established for a nonlinear ν th order At ı c ı -Eloe fractional difference equation, Δ ν u ( t )+ f ( u ( t + ν − 1 )) = 0, t ∈ { 1 , 2 ,..., T + 1 } , satisfying the Dirichlet boundary conditions u ( ν − 2 ) = u ( ν + T + 1 ) = 0 ,