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 $f^{\left(k\right)}+B_{k-1}\left(z\right)f^{(k-1)}+\cdots +B_1\left(z\right)f^{\prime }+B_0\left(z\right)f=0$, where $k\ge 2$ 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].

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