Perturbation of zeros of solutions to second order differential equations with polynomial coefficients

Let P  (z) and P˜(z) be polynomials of the same degree. We consider the equations u″ = P(z)u   and u˜′′=P˜(z)u˜  (z∈ℂ) whose solutions are u(z) and u˜(z), respectively. Let zk  (u) and zk(u˜),k=1,2,…, be the zeros of u(z) and u˜(z), respectively. We derive bounds for the quantity kinf|1zk(u)−1zj(u˜)|.