Further results on the exponent of convergence of zeros of solutions of certain higher order linear differential equations

Abstract

In this paper, we further investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $$ f^{(k)}+a_{k-1}(z)f^{(k-1)}+\cdots+a_1(z)f' +\psi(z)f=0, $$ where $\psi(z)=\sum_{j=1}^\iota Q_j(z)e^{P_j(z)} (\iota\geq 3, \iota\in N_+ )$, $P_j(z)$ are polynomials of degree $n\geq1$, $Q_j(z),a_\Lambda(z)(\Lambda=1,2,\cdots,k-1;j=1,2,\ldots,\iota)$ are entire functions of order less than $n$, and $k\geq2$.