Oscillation results for solutions of linear differential equations in the complex domain (Q917750)

The authors continue their study of the exponent of convergence \(\lambda\) (f) of the zero-sequence of nontrivial solutions f(z) to \((E)\quad y''+A(z)y=0,\) where A(z) is a transcendental entire function. An example is the following perturbation theorem: Theorem. Let A(z) be a transcendental entire function of finite integral order \(\sigma\geq 1\) and let \(f_ 1(z)\) and \(f_ 2(z)\) be two linearly independent solutions of (E) such that \(\max (\lambda (f_ 1),\lambda (f_ 2))<\sigma.\) Then for any nontrivial entire function \(\Pi\) (z) of order \(\sigma (\Pi)<\sigma\) and any two linearly independent solutions \(g_ 1(z)\) and \(g_ 2(z)\) of the equation \(y''+[A(z)+\Pi (z)]y=0,\max (\lambda (g_ 1),\lambda (g_ 2))\geq \sigma.\) Results are also given for equations of the form \(y''+[Re^ P+Se^ Q+T]y=0,\) when P, Q, R, S, and T are polynomials.