Geodesic
On the Growth and the Zeros of Solutions of Higher Order Linear Differential Equations with Meromorphic Coefficients
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 199

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We investigate the growth of meromorphic solutions of homogeneous and nonhomogeneous higher order linear differential equations $ f^{(k)}+um_{j=1}^{k-1}A_jf^{(j)}+A_0f=0\;\;(k\geqslant 2), $ $ f^{(k)}+um_{j=1}^{k-1}A_jf^{(j)}+A_0f=A_k\;\;(k\geqslant 2), $ where $A_j(z)$ ($j=0,1,\dots,k$) are meromorphic functions with finite order. Under some conditions on the coefficients, we show that all meromorphic solutions $f\not\equiv 0$ of the above equations have an infinite order and infinite lower order. Furthermore, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. We improve the results due to Kwon; Chen and Yang; Bela\'{\i}di; Chen; Shen and Xu.
DOI : 10.2298/PIM141009007A
Classification : 34M10 30D35
Keywords: linear differential equations, meromorphic functions, order of growth, hyper-order, exponent of convergence of zeros, hyper-exponent of convergence of zeros 
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     author = {Maamar Andasmas and Benharrat Bela and i di},
     title = {On the {Growth} and the {Zeros} of {Solutions} of {Higher} {Order} {Linear} {Differential} {Equations} with {Meromorphic} {Coefficients}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {199 },
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Maamar Andasmas; Benharrat Bela; i di. On the Growth and the Zeros of Solutions of Higher Order Linear Differential Equations with Meromorphic Coefficients. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 199 . doi: 10.2298/PIM141009007A

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