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

We gave the calculate formula for characteristic multiplier of Hill's equation x″+q(t)x=0x″+q(t)x=0 in case q(t)>0q(t)>0 and q(t)<0q(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)<0q(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)q(t) alternate signs and ∫0πq(t)dt>0.