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 = 0has at most one zero in D. We show that if A = Q exp P where P and Qare polynomials, one can usually take D to be an angle of opening Π/n where n isthe degree of P.