Complex Linear Differential Equations with Analytic Coefficients of Iterated Order in the Annulus

Abstract

In this paper, we study the growth properties of solutions of the linear differential equations
f^(k) + B_k−1 (z) f^(k−1) + · · · + B₁ (z) f′ + B₀ (z) f = 0,
f^(k) + B_k−1 (z) f^(k−1) + · · · + B₁ (z) f′ + B₀ (z) f = F,
where B_k−1 (z) , ...,B₀ (z) and F (z) are analytic functions of iterated order in an annulus. We obtain some results concerning the estimates of the iterated order of solutions of the above equations.

Key words and phrases. Linear differential equations, analytic solutions, Annulus, iterated order.

2010 Mathematics Subject Classification. 30D10; 30D20; 30B10; 34M05