Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations

Abstract

The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+ Af0+ Bf= F, where A (z), B (z) and F (z) are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ> 0, α> 0 such that| A (z)|≥ eα| z| σ as| z|→+∞, z∈ H, where dens {| z|: z∈ H}> 0 and ρ= max {ρ (B), ρ (F)}< σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.