On the zeros of solutions of a class of second order linear differential equations

Abstract

In this paper, we investigate the exponent of convergence of the zero-sequence of solutions of the second order linear differential equation

$$f''+\left(\sum_{j=1}^{l}Q_j(z)e^{P_j(z)}\right)f=0,$$

where P_j (z) (j= 1,2, ..., l ≥ 3) are polynomials of degree n ≥ 1, Q_j (z) are entire functions of order less than n, and obtain some results which improve and generalize the previous results in [8, 9, 13].