On oscillation theorems for differential polynomials
In this paper, we investigate the relationship between small functions and differential polynomials $g_{f}\left( z\right)=d_{2}f^{^{\prime \prime }} + d_{1}f^{^{\prime }}+d_{0}f$, where $d_{0}\left(z\right), d_{1}\left( z\right), d_{2}\left( z\right) $ are meromorphic functions that are not all equa...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
University of Szeged
2009-04-01
|
Series: | Electronic Journal of Qualitative Theory of Differential Equations |
Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=375 |
Summary: | In this paper, we investigate the relationship between small functions and differential polynomials $g_{f}\left( z\right)=d_{2}f^{^{\prime \prime }} + d_{1}f^{^{\prime }}+d_{0}f$, where $d_{0}\left(z\right), d_{1}\left( z\right), d_{2}\left( z\right) $ are meromorphic functions that are not all equal to zero with finite order generated by solutions of the second order linear differential equation
\begin{equation*}
f^{^{\prime \prime }}+Af^{^{\prime }}+Bf=F,
\end{equation*}
where $A,$ $B,$ $F\not\equiv 0$ are finite order meromorphic functions having only finitely many poles. |
---|---|
ISSN: | 1417-3875 |