In this paper we obtain the following theorenms:THEOREM l:Let A(z) be a finite-order σ>0 meromorphic function. Suppose that the second order linear diferential equation possesses two lineary independent solutions y1

y2 such that (1) P is a σ-degree polynomial;(2) Q1. Q2 are meromorphic functions of order less than σ andQ2=THEOREM 2: Let A(z) be a finite - order σ>0 meromorphic function. Let f1

f2 be two linearly independent solutions of (1)such that (2) holds. Then for any meromorphic function B (z) 0 of order σ(B)0. Let Q be a meromorphic function of T(r

Q ) = 0{t(r

eP)}. Suppose that the differential equation yn+(eP + Q )y= 0 possesses a non - trivial solution y such that max {λ(y) .λ(y1)} 0 entire function. Suppose that (1) possesses two linearly independent solutions y1

y2 such that max {λ(y1)

λ(y2)}