{"title":"一类高阶线性微分-差分方程亚纯解的生长性质","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":"{\"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}","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}
Growth properties of meromorphic solutions of some higher-order linear differential-difference equations
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.