关于二阶线性微分方程解的增长性
On The Growth of Solutions of Second Order Linear Differential Equations
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摘要: 研究了二阶微分方程~f''+A_1(z)P(e^z)f'+A_0(z)Q(e^z)f=0~和~f''+(A_1(z)P(e^z)+D_1(z))f'\\+(A_0(z)Q(e^z)+D_0(z))f=0~ 解的增长性，其中~P(e^z)~与~Q(e^z)~是~e^z~的非常数多项式，它们的常数项\\都为零，且次数不相等.~证明了该方程的每个非零解有无穷级.Abstract: The growth of solutions of the differential equations f''+A_1(z)P(e^z)f'+A_0(z)Q(e^z)f=0 and f''+(A_1P(e^z)+D_1(z))f'+(A_0Q(e^z)+D_0(z))f=0 is investigated, where~P(e^z)~and~Q(e^z)~are nonconstant polynomials without constants, and degP is not equal to degQ. It is showed that the order of growth of each nonzero solution of the above equations is infinite.
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