The calculation for characteristic multiplier of Hill's equation x '' plus q(t)x=0 in case q(t) with positive mean

摘要

We gave the calculate formula for characteristic multiplier of Hill's equation x" + q(t)x = 0 in case q(t) > 0 and q(t) < 0 in the papers of Shi et al. [The calculation for characteristic multiplier of Hill's equation, Appl. Math. Comput. 159 (2004) 57-77] and Shi et al. [The calculation for characteristic multiplier of Hill's equation in case q(t) < 0, 167 (2005) 1130-1149], respectively. In this paper, we give the calculate formula for characteristic multiplier of Hill's equation in case q(t) alternate signs and integral(pi)(0) q(t) dt > 0. (C) 2007 Elsevier Ltd. All rights reserved.