一类周期线性微分方程的复振荡

ONE CLASS OF COMPLEX OSCILLATION OF PERIODIC LINEAR DIFFERENTIAL EQUATIONS

证明了周期方程f(4)+K2f''+K1f'+(ez+K0)f=0具有一个有限零点收敛指数的解的必要条件是 ,且满足某一(k+1)×(k+1)行列式条件,其中k是一个非负整数.其次得到这种解的明显表示.进一步,对于四阶周期方程证明了CHIANGYikman和WANG Shuipei的一个猜想.

It is verified that the necessary condition for the periodic equation f(4)+f2f'+K1f'+ (ez+ K0)f = 0 to adimit a solution with finite exponent of convergence of zeros is where k is a nonnegative integer satisfying some (k + l)×(k+l) determinant condition. An explicit representation for such a solution is obtained. Moreover, a conjecture of Chiang Yikman and Wang Shuipei for a fourth order periodic equation is proved.