Growth properties of solutions to higher order complex linear differential equations with analytic coefficients in the annulus

Benharrat Belaïdi

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 19-35

Résumé

In this paper, by using the Nevanlinna value distribution theory of meromorphic functions on an annulus, we deal with the growth properties of solutions of the linear differential equation $ f^{\left( k\right) }+B_{k-1}\left( z\right) f^{\left( k-1\right) }+\cdots +B_{1}\left( z\right) f^{\prime }+B_{0}\left( z\right) f=0$, where $k\geq 2$ is an integer and $B_{k-1}\left( z\right),\dots,B_{1}\left( z\right) ,B_{0}\left( z\right) $ are analytic on an annulus. Under some conditions on the coefficients, we obtain some results concerning the estimates of the order and the hyper-order of solutions of the above equation. The results obtained extend and improve those of Wu and Xuan in [16].