Abstract
In this paper, we investigate the growth and fixed points of meromorphic solutions and their derivatives of higher-order nonhomogeneous linear differential equations with meromorphic coefficients. Our results extend the previous theorems due to Gundersen and Yang, Han and Yi. As an application of our results, we generalized some previous results that are related to Brück’s conjecture.MSC:34M10, 30D35.
Highlights
1 Introduction and main results In this paper, we shall assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions
In order to give some estimates of fixed points, we recall the following definitions
Every meromorphic solution f ≡, whose poles are of uniformly bounded multiplicities, of the equation f (k) – R(z)eP(z)f = Q(z) has infinite order and satisfies λ (f ) = λ(f ) = ρ(f ) = ∞
Summary
Introduction and main resultsIn this paper, we shall assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions (see [ – ]). Every meromorphic solution f ≡ , whose poles are of uniformly bounded multiplicities, of the equation f (k) – R(z)eP(z)f = Q(z) has infinite order and satisfies λ (f ) = λ(f ) = ρ(f ) = ∞. Let P(z) be a nonconstant polynomial, R(z) (≡ ), Q(z) (≡ ) be meromorphic functions that have finitely many poles and max{ρ(R), ρ(Q)} < deg(P) = n and k be a positive integer.
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