Growth of Meromorphic Solutions of a class of Higher Order Linear Differential Equations
Abstract
In this paper, we investigate the order and the hyper-order of meromorphic solutions of the linear differential equation f^{(k)}+∑(B_{j}e^{P_{j}(z)}+D_{j}e^{R_{j}(z)})f^{(j)}+(Aâ‚e^{Qâ‚(z)}+Aâ‚‚e^{Qâ‚‚(z)})f=0,where Q_{s}(z) (s=1,2), P_{j}(z), R_{j}(z) (j=1,...,k-1) are nonconstant polynomials and A_{s}(z) (s=1,2), B_{j}(z), D_{j}(z) (j=1,...,k-1) are meromorphic functions (≡0). Under some conditions, we prove that every meromorphic solution f(≡0) of the above equation is of infinite order and we give an estimate of its hyper-order.
Published
2020-02-24
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How to Cite
Growth of Meromorphic Solutions of a class of Higher Order Linear Differential Equations. (2020). Nonlinear Studies, 27(1). https://www.nonlinearstudies.com/index.php/nonlinear/article/view/1369