Oscillation of solutions of some higher order linear differential equations.

Xu, Hong-Yan; Cao, Ting-Bin

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In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation $\begin{matrix} f^{(k)} + A_{k - 1} f^{(k - 1)} + \dots + A_{2} f^{''} + (D_{1} (z) + A_{1} (z) e^{a z}) f^{'} \\ + (D_{0} (z) + A_{0} (z) e^{b z}) f = F (k \geq 2), \end{matrix}$ where $a$ , $b$ are complex constants that satisfy $a b (a - b) \neq 0$ and $A_{j} (z)$ $(j = 0, 1, \dots, k - 1)$ , $D_{j} (z)$ $(j = 0, 1)$ , $F (z)$ are entire functions with $max {ρ (A_{j}) (j = 0, 1, \dots, k - 1), ρ (D_{j})$ $(j = 0, 1)} < 1$ . We also investigate the relationship between small functions and the solutions of the above equation.