On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients
We consider that the linear differential equations f(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0, where Aj (j=0,1,…,k-1), are entire functions. Assume that there exists l∈{1,2,…,k-1}, such that Al is extremal for Yang's inequality; then we will give some conditions on other coefficients which can guar...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/305710 |
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| _version_ | 1832545961375694848 |
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| author | Jianren Long Chunhui Qiu Pengcheng Wu |
| author_facet | Jianren Long Chunhui Qiu Pengcheng Wu |
| author_sort | Jianren Long |
| collection | DOAJ |
| description | We consider that the linear differential equations f(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0, where Aj (j=0,1,…,k-1), are entire functions. Assume that there exists l∈{1,2,…,k-1}, such that Al is extremal for Yang's inequality; then we will give some conditions on other coefficients which can guarantee that every solution f(≢0) of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder of f if every solution f(≢0) of the equation is of infinite order. |
| format | Article |
| id | doaj-art-f3849e569e254738b35fda7e3113d829 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f3849e569e254738b35fda7e3113d8292025-02-03T07:24:21ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/305710305710On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal CoefficientsJianren Long0Chunhui Qiu1Pengcheng Wu2School of Mathematical Sciences, Xiamen University, Xiamen 361005, ChinaSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, ChinaSchool of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, ChinaWe consider that the linear differential equations f(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0, where Aj (j=0,1,…,k-1), are entire functions. Assume that there exists l∈{1,2,…,k-1}, such that Al is extremal for Yang's inequality; then we will give some conditions on other coefficients which can guarantee that every solution f(≢0) of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder of f if every solution f(≢0) of the equation is of infinite order.http://dx.doi.org/10.1155/2014/305710 |
| spellingShingle | Jianren Long Chunhui Qiu Pengcheng Wu On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients Abstract and Applied Analysis |
| title | On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients |
| title_full | On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients |
| title_fullStr | On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients |
| title_full_unstemmed | On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients |
| title_short | On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients |
| title_sort | on the growth of solutions of a class of higher order linear differential equations with extremal coefficients |
| url | http://dx.doi.org/10.1155/2014/305710 |
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