On the zeros of solutions of differential equation \(f''+Af=0\) (Q1196588)

In the paper the linear differential equation of the second order (1) \(f''+Af=0\) is studied. The following theorem is proved: Let \(A\) be a transcendental entire function of the lower order \(\nu<\infty\) with \(k\) distinct finite asymptotic values. Let \(k=2\nu\). If \(f_ 1\), \(f_ 2\) are two linearly independent solutions of (1), then \(\max(\lambda(f_ 1),\lambda(f_ 2))=\infty\) where \(\lambda(f)\) denotes the exponent of convergence of zeros of \(f\).