Schwarzian Derivatives and Zeros of Solutions to Second Order Linear Differential Equations

Let A be entire. Suppose that there exists an unbounded quasidisk D such that A is sufficiently small in D. We prove that then any nontrivial solution to y" + Ay = 0 has at most one zero in D. We show that if A = Q exp P where P and Q are polynomials, one can usually take D to be an angle of opening x/n where n is the degree of P .