Abstract
In this note we study the value distribution of solutions of certain difference equations analogous to differential equations, the finite order solutions of which do not have wandering domains. Meanwhile, the nonexistence of wandering domains of solutions with finite order of these difference equations is proved. Thus the nonexistence of wandering domains of solutions of these difference and differential equations is similar in some extent.
Highlights
Introduction and main resultsLet f be a nonlinear meromorphic function, the Fatou set F(f ) is the set of points z ∈ C such that iterates of f, (f n)n∈N, form a normal family in some neighborhood of z
In [ ], the nonexistence of wandering domains is proved by Wang for a meromorphic function f of finite order satisfying some first order nonlinear differential equations, see the following two theorems
We study the value distribution and dynamical properties of the solutions of difference equations which are analogous to differential equations ( ) and ( )
Summary
Introduction and main resultsLet f be a nonlinear meromorphic function, the Fatou set F(f ) is the set of points z ∈ C such that iterates of f , (f n)n∈N, form a normal family in some neighborhood of z. In [ ], the nonexistence of wandering domains is proved by Wang for a meromorphic function f of finite order satisfying some first order nonlinear differential equations, see the following two theorems. Suppose that f is a meromorphic solution of the differential equation f n = q(z)p(f ) f – a t(f – z)m. Theorem B Let q(z) be a rational function, p(z), Q(z) be two polynomials and m, n ∈ N.
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