EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 98(112), pp. 199–210 (2015)

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On the growth and the zeros of solutions of higher order linear differential equations with meromorphic coefficients

Maamar Andasmas, Benharrat Belaïdi

Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), Mostaganem, Algeria

Abstract: We investigate the growth of meromorphic solutions of homogeneous and nonhomogeneous higher order linear differential equations $$ f^{(k)}+\sum_{j=1}^{k-1}A_jf^{(j)}+A_0f=0 (k\geqslant 2), $$ $$ f^{(k)}+\sum_{j=1}^{k-1}A_jf^{(j)}+A_0f=A_k (k\geqslant 2), $$ 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.

Keywords: linear differential equations; meromorphic functions; order of growth; hyper-order; exponent of convergence of zeros; hyper-exponent of convergence of zeros

Classification (MSC2000): 34M10; 30D35

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Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.

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