| Title:
|
On the growth of solutions of some higher order linear differential equations (English) |
| Author:
|
El Farissi, Abdallah |
| Author:
|
Belaidi, Benharrat |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
377-390 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation \begin{align} &f^{(k)}+A_{k-1}f^{(k-1)}+\dots +A_{2}f''+(D_{1}(z) +A_{1}(z) {\rm e}^{az})f'\\ &\hfill +( D_{0}(z)+A_{0}(z) {\rm e}^{bz}) f=F\quad (k\ge 2), \end{align} where $a$, $b$ are complex constants that satisfy $ab(a-b) \neq 0 $ and $A_{j}(z)$ $(j=0,1,\dots ,k-1)$, $D_{j}(z) $ $(j=0,1)$, $F(z) $ are entire functions with $\max \{\rho (A_{j}) \ (j=0,1,\dots ,k-1), \ \rho (D_{j})$ $(j=0,1)\}<1$. We also investigate the relationship between small functions and the solutions of the above equation. (English) |
| Keyword:
|
linear differential equations |
| Keyword:
|
entire solutions |
| Keyword:
|
order of growth |
| Keyword:
|
exponent of convergence of zeros |
| Keyword:
|
exponent of convergence of distinct zeros |
| MSC:
|
30D35 |
| MSC:
|
34M03 |
| MSC:
|
34M10 |
| idZBL:
|
Zbl 1265.34327 |
| idMR:
|
MR2984609 |
| DOI:
|
10.1007/s10492-012-0022-y |
| . |
| Date available:
|
2012-08-19T21:46:00Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142905 |
| . |
| Reference:
|
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| Reference:
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