| Title:
|
Complex Oscillation Theory of Differential Polynomials (English) |
| Author:
|
El Farissi, Abdallah |
| Author:
|
Belaïdi, Benharrat |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
43-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we investigate the relationship between small functions and differential polynomials $g_{f}(z)=d_{2}f^{\prime \prime }+d_{1}f^{\prime }+d_{0}f$, where $d_{0}(z)$, $d_{1}(z)$, $d_{2}(z)$ are entire functions that are not all equal to zero with $\rho (d_j)<1$ $(j=0,1,2) $ generated by solutions of the differential equation $f^{\prime \prime }+A_{1}(z) e^{az}f^{\prime }+A_{0}(z) e^{bz}f=F$, where $a,b$ are complex numbers that satisfy $ab( a-b) \ne 0$ and $A_{j}( z) \lnot \equiv 0$ ($j=0,1$), $F(z) \lnot \equiv 0$ are entire functions such that $\max \left\lbrace \rho (A_j),\, j=0,1,\, \rho (F)\right\rbrace <1.$ (English) |
| Keyword:
|
linear differential equations |
| Keyword:
|
differential polynomials |
| Keyword:
|
entire solutions |
| Keyword:
|
order of growth |
| Keyword:
|
exponent of convergence of zeros |
| Keyword:
|
exponent of convergence of distinct zeros |
| MSC:
|
30D35 |
| MSC:
|
34M10 |
| idZBL:
|
Zbl 1244.34108 |
| idMR:
|
MR2920698 |
| . |
| Date available:
|
2011-12-08T09:47:45Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141721 |
| . |
| Reference:
|
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| Reference:
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