On the Order of Growth of Solutions to Complex Nonhomogeneous Linear Differential Equations
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In this paper, we study the order ofgrowth of solutions to the non-homogeneous linear differential equation\begin{equation*}f^{\left( k\right) }+A_{k-1}e^{az}f^{\left( k-1\right) }+\cdots+A_{1}e^{az}f^{\prime }+A_{0}e^{az}f=F_{1}e^{az}+F_{2}e^{bz},\end{equation*}where $A_{j}\left( z\right) $ $\left( \not\equiv 0\right) $ $\left(j=0,1,\cdots ,k-1\right) $, $F_{j}\left( z\right) $ $\left( \not\equiv0\right) $ $\left( j=1,2\right) $ are entire functions and $a$, $b$ arecomplex numbers such that $ab\left( a-b\right) \neq 0$.
Abstract
In this paper, we study the order ofgrowth of solutions to the non-homogeneous linear differential equation\begin{equation*}f^{\left( k\right) }+A_{k-1}e^{az}f^{\left( k-1\right) }+\cdots+A_{1}e^{az}f^{\prime }+A_{0}e^{az}f=F_{1}e^{az}+F_{2}e^{bz},\end{equation*}where $A_{j}\left( z\right) $ $\left( \not\equiv 0\right) $ $\left(j=0,1,\cdots ,k-1\right) $, $F_{j}\left( z\right) $ $\left( \not\equiv0\right) $ $\left( j=1,2\right) $ are entire functions and $a$, $b$ arecomplex numbers such that $ab\left( a-b\right) \neq 0$.
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