OSCILLATION RESULTS OF CERTAIN HIGHER-ORDER LINEAR-DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS IN THE COMPLEX-PLANE

Baesch (Results in Math. 29, 1996, 42-55) has given a characterization of homogeneous linear differential equations with certain analytic pe riodic coefficients which admits a solution with finite exponent of co nvergence. However, her method seems too general and in most cases too complicated for applications. We give, in this paper, a direct approa ch to the problem and obtain several such characterizations which do n ot seem to follow from those of Baesch. In particular, an explicit, ne cessary and sufficient condition to the problem is given for certain t hird order equations. The results again do not seem to follow from tho se of Baesch. Our method is based on that of Y. M. Chiang, I. Laine, a nd S. Wang (Complex Variables, 34 (1997), 25-34) which in turn depends on basic representations of solutions given by Bank, Laine, and Langl ey. (C) 1997 Academic Press.