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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/305710 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |