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∈) whose solutions are u(z) and u ̃(z), respectively. Let . z k(u) and zk(u tild;),k=1,2,..., be the zeros of u(z) and u ̃(z), respectively. We derive bounds for the quantity. kinf|1zk(u)-1zj(u ̃)|.
- Complex differential equation
- Perturbation of zeros
- Zeros of solutions