Turkish Journal of Mathematics
Article Title
On the growth of meromorphic solutions of some higher order linear differential equations
DOI
10.3906/mat-1701-62
Abstract
Let $k,m,n $ be integers such that $k\geq 1$, $n\geq 2$ and $1\leq m\leq n$. In this article we study the order $\rho(f)$ and the hyperorder $\rho_2(f)$ of nonzero meromorphic solutions $f$ of the differential equation $$\sum_{j=1,j\ne m}^{n}A_j(z)f^{(j)}(z)+A_m(z)e^{p_m(z)}f^{(m)}(z)+\left(A_0(z)e^{p(z)}+B_0(z)e^{q(z)}\right)f(z)=0,$$ where $B_0(z)$, $A_0(z), \cdots, A_n(z)$ are meromorphic functions such that $A_0A_mA_nB_0\not\equiv 0$, $\max\{\rho(B_0), \rho(A_0), \cdots,\rho(A_n)\}
Keywords
Meromorphic functions, Nevanlinna value distribution theory, linear differential equation, order of growth
First Page
1049
Last Page
1059
Recommended Citation
MESBOUT, FARID and ZERZAIHI, TAHAR
(2018)
"On the growth of meromorphic solutions of some higher order linear differential equations,"
Turkish Journal of Mathematics: Vol. 42:
No.
3, Article 25.
https://doi.org/10.3906/mat-1701-62
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss3/25
