{"title":"Growth properties of meromorphic solutions of some higher-order linear differential-difference equations","authors":"Rachid Bellaama, B. Belaïdi","doi":"10.1515/anly-2021-1000","DOIUrl":null,"url":null,"abstract":"Abstract This paper is devoted to the study of the growth of meromorphic solutions of homogeneous and non-homogeneous linear differential-difference equations ∑ i = 0 n ∑ j = 0 m A i j f ( j ) ( z + c i ) = 0 , \\displaystyle\\sum_{i=0}^{n}\\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=0, ∑ i = 0 n ∑ j = 0 m A i j f ( j ) ( z + c i ) = F , \\displaystyle\\sum_{i=0}^{n}\\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F, where A i j {A_{ij}} ( i = 0 , … , n {i=0,\\ldots,n} , j = 0 , … , m {j=0,\\ldots,m} ), F are meromorphic functions and c i {c_{i}} ( 0 , … , n {0,\\ldots,n} ) are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng.","PeriodicalId":82310,"journal":{"name":"Philosophic research and analysis","volume":"116 1","pages":"71 - 88"},"PeriodicalIF":0.0000,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophic research and analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/anly-2021-1000","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This paper is devoted to the study of the growth of meromorphic solutions of homogeneous and non-homogeneous linear differential-difference equations ∑ i = 0 n ∑ j = 0 m A i j f ( j ) ( z + c i ) = 0 , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=0, ∑ i = 0 n ∑ j = 0 m A i j f ( j ) ( z + c i ) = F , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F, where A i j {A_{ij}} ( i = 0 , … , n {i=0,\ldots,n} , j = 0 , … , m {j=0,\ldots,m} ), F are meromorphic functions and c i {c_{i}} ( 0 , … , n {0,\ldots,n} ) are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng.