Translator Disclaimer
February 2010 Growth of solutions and oscillation of differential polynomials generated by some complex linear differential equations
Benharrat BELAÏDI, Abdallah EL FARISSI
Hokkaido Math. J. 39(1): 127-138 (February 2010). DOI: 10.14492/hokmj/1274275023

Abstract

This paper is devoted to studying the growth and the oscillation of solutions of the second order non-homogeneous linear differential equation $$ f''+A_{1} (z) e^{P (z)}f'+A_{0} (z) e^{Q (z)}f = F, $$ where $P (z)$, $Q (z)$ are nonconstant polynomials such that $\deg P=\deg Q=n$ and $A_{j} (z)$ $( \not\equiv 0 )$ $(j=0,1)$, $F\not\equiv 0$ are entire functions with $\rho ( A_{j} ) < n$ $( j=0,1 )$. We also investigate the relationship between small functions and differential polynomials $g_{f} (z)=d_{2}f''+d_{1}f'+d_{0}f$, where $d_{0} (z)$, $d_{1} (z)$, $d_{2} (z)$ are entire functions that are not all equal to zero with $\rho ( d_{j} ) < n$ $( j=0,1,2 )$ generated by solutions of the above equation.

Citation

Download Citation

Benharrat BELAÏDI. Abdallah EL FARISSI. "Growth of solutions and oscillation of differential polynomials generated by some complex linear differential equations." Hokkaido Math. J. 39 (1) 127 - 138, February 2010. https://doi.org/10.14492/hokmj/1274275023

Information

Published: February 2010
First available in Project Euclid: 19 May 2010

zbMATH: 1201.34136
MathSciNet: MR2649330
Digital Object Identifier: 10.14492/hokmj/1274275023

Subjects:
Primary: 34M10
Secondary: 30D35

Rights: Copyright © 2010 Hokkaido University, Department of Mathematics

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.39 • No. 1 • February 2010
Back to Top