On the growth of meromorphic solutions of some higher order linear differential equations

Authors : Farid MESBOUT, Tahar ZERZAIHI

Pages : 1049-1059

View : 9 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

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 $\rhoinsert ignore into journalissuearticles values(f);$ and the hyperorder $\rho_2insert ignore into journalissuearticles values(f);$ of nonzero meromorphic solutions $f$ of the differential equation $$\sum_{j=1,j\ne m}^{n}A_jinsert ignore into journalissuearticles values(z);f^{insert ignore into journalissuearticles values(j);}insert ignore into journalissuearticles values(z);+A_minsert ignore into journalissuearticles values(z);e^{p_minsert ignore into journalissuearticles values(z);}f^{insert ignore into journalissuearticles values(m);}insert ignore into journalissuearticles values(z);+\leftinsert ignore into journalissuearticles values(A_0insert ignore into journalissuearticles values(z);e^{pinsert ignore into journalissuearticles values(z);}+B_0insert ignore into journalissuearticles values(z);e^{qinsert ignore into journalissuearticles values(z);}\right);finsert ignore into journalissuearticles values(z);=0,$$ where $B_0insert ignore into journalissuearticles values(z);$, $A_0insert ignore into journalissuearticles values(z);, \cdots, A_ninsert ignore into journalissuearticles values(z);$ are meromorphic functions such that $A_0A_mA_nB_0\not\equiv 0$, $\max\{\rhoinsert ignore into journalissuearticles values(B_0);, \rhoinsert ignore into journalissuearticles values(A_0);, \cdots,\rhoinsert ignore into journalissuearticles values(A_n);\}
Keywords : Meromorphic functions, Nevanlinna value distribution theory, linear differential equation, order of growth