ON THE ASYMPTOTIC BEHAVIOR OF THE ZEROS OF SOLUTIONS TO w" + Aw = 0
We study the asymptotic behavior of the zeros of solutions to vi" + Au; = 0 where A(z) = J ^ j i i Qj{z)expPj(z) with Qj and Pj polynomials in z. Under mild hypotheses on the Pj's and Qj'a, we identify algebraic curves ahout which the zeros of solutions düster. The curves are of the form Im P{z) = K with P a polynomial and K a constant. We determine a bound for the rate of approach of the zeros to these curves. In addition to classical techniques of ordinary differential equations, we employ methods developed by W. Strödt [8], Strodt's general theory examines the existence and asymptotic behavior of solutions to certain first order differential equations in the complex domain. AMS Classification: 34A20, 34C10.