【摘要】 本文得到如下主要结果:设 P（z）和 Q（s）为多项式,degP=m>0。若方程f″+(e^P（z）)+Q（z）)f=0存在一非平凡解 f,使得λ（f）<m,则 Q=-1/（16）P′²+1/4P″;反之亦然（其中λ（f）表示 f 的零点收敛指数）。更多还原

【Abstract】 It is shown that if the differential equation f″+(e~p +Q)f=0 (1) (where P and Q are polynomials with deg P>0) possesses a non-trivial solution with λ(f);<deg P,then Q=-1/(16)P′~2+1/4 P″。(2) Conversely,if Q satisfies (2),then (1) has a non-trivial solution with λ(f)=0 (where λ(f) denotes the exponent of eonvergence of the zero-sequence of f(z)).更多还原