Iterated order of meromorphic soloutions of homogeneous and nonhomogeneous linear differential equations

Abstract

In this paper, we investigate the iterated order of meromorphic solutions of homogeneous and non-homogeneous to higher order linear differential equations f (k) + Σk−1 j=1 Aj f ( j) + A0 f = 0 (k > 2) , f (k) + Σk−1 j=1 Aj f ( j) + A0 f = F (k > 2) , where Aj (z) ( j = 0, 1, · · · , k − 1) and F (z) are meromorphic functions with finite iterated p−order. Under some conditions on the coefficients, we show that all meromorphic solutions f . 0 of the above equations have an infinite iterated p−order and infinite iterated lower p−order. Furthermore, we give some estimates of iterated convergence exponent. We improve the results due to Chen; Shen and Xu; He, Zheng and Hu and others.