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Keywords:
linear differential equations; entire solutions; order of growth; exponent of convergence of zeros; exponent of convergence of distinct zeros
linear differential equations; entire solutions; order of growth; exponent of convergence of zeros; exponent of convergence of distinct zeros
Summary:
In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation \begin{align} &f^{(k)}+A_{k-1}f^{(k-1)}+\dots +A_{2}f''+(D_{1}(z) +A_{1}(z) {\rm e}^{az})f'\\ &\hfill +( D_{0}(z)+A_{0}(z) {\rm e}^{bz}) f=F\quad (k\ge 2), \end{align} where $a$, $b$ are complex constants that satisfy $ab(a-b) \neq 0 $ and $A_{j}(z)$ $(j=0,1,\dots ,k-1)$, $D_{j}(z) $ $(j=0,1)$, $F(z) $ are entire functions with $\max \{\rho (A_{j}) \ (j=0,1,\dots ,k-1), \ \rho (D_{j})$ $(j=0,1)\}<1$. We also investigate the relationship between small functions and the solutions of the above equation.
References:
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