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

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Maamar Andasmas
Benharrat Belaidi

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 Ï = max{Ï(B), Ï(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.

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References

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