一类二阶线性微分方程解的增长性

本文研究一类二阶齐次线性微分方程f"+A_1(z)e~(P(z))f'+A_0(z)e~(Q(z))f=0,解的增长性,其中P(z)=az~n,Q(z)=bz~n,ab≠0,a=cb(c1),A_j(z)(j=0,1)是非零多项式,证明了该方程的每个非零解满足σ(f)=∞并且σ_2(f)=n.

On the Growth of Solutions to Some Second Order Linear Differential Equations

The authors investigate the growth of solutions to some second-order differential equations \begin{align*} f'+A_{1}(z)\rme^{P(z)}f'+A_{0}(z)\rme^{Q(z)}f=0, \end{align*} where $P(z)=az^{n}$, $Q(z)=bz^{n}$, $ab\neq{0}$, $a=cb~(c>1)$, and $A_{j}(z)\ (j=0, 1)$ are non-zero polynomials. It is obtained that every non-zero solution $f$ of the above equation satisfies $\sigma(f)=\infty$ and $\sigma_{2}(f)=n$.