【摘要】 运用Nevunlinna值分布理论和整函数的相关理论,研究了2类不同系数的2阶线性微分方程解的增长性.假设A(z)=h(z)eP1(z),其中P1(z)是m次多项式,h(z)是ρ(h)<m的整函数,B(z)是1个级为ρ(B)≠m的超越整函数,证明了方程f″+Af’+Bf=0的每1个非零解都是无穷级;又假设A(z)是方程f″+P2(z)f=0的非零解,其中P2(z)是n次多项式,B(z)是Fabry缺项级数且2ρ(B)≠n+2,也证明了方程f″+Af’+Bf=0的每1个非零解都具有无穷级.更多还原

【Abstract】 By using the Nevunlinna theory and the theory of entire functions,the growth of solutions of the second order linear differential equations with two different coefficients is considered. Let A( z) = h( z) eP1( z)be an entire function,where P1( z) is a polynomial of m degree and h( z) is an entire function of order ρ( h) < m,and let B( z)be a transcendental entire function of order ρ( B) ≠m. Then every nontrivial solution of f ″ + Af ’ + Bf = 0 is of infinite order. Similarly,let A( z) be a nontrivial solution of f ″ + P2( z) f = 0,where P2( z) is a polynomial of degree and let B( z) be the Fabry gap series of order ρ( B) ≠( n + 2) 2. Then every nontrivial solution of f ″ + Af ’ + Bf = 0 is also of infinite order.更多还原