[PDF] Top 20 The zeros of difference of meromorphic solutions for the difference Riccati equation

... Recently, a number of papers (including [–]) focused on complex difference equa- tions and difference analogs of Nevanlinna’s theory. As the difference analogs of Nevan- linna’s theory were being investigated, many ... See full document

... investigate zeros and α -points of meromorphic solutions f(z) for difference Riccati equations, and we obtain some estimates of exponents of convergence of zeros and α -points of f (z) ... See full document

... We assume that the reader is familiar with the standard notations and results of Nevan- linna value distribution theory (see, e.g., [–]). Let w be a meromorphic function in the complex plane. ρ(w), λ(w) and ... See full document

... A finite value a is called the Picard exceptional value of f, if f - a has no zeros. The Picard theorem shows that a transcendental entire function has at most one Picard exceptional value, a transcendental ... See full document

... A meromorphic function α(z) is called a small function with respect to f (z), if T(r, α) = S(r, f ), where S(r, f ) denotes any quantity satisfying S(r, f ) = o(T (r, f )) as r → ∞ outside a possible exceptional ... See full document

... and meromorphic in the ...the meromorphic function f (z), and λ(f ) and λ(  f ) to denote, respectively, the exponents of convergence of zeros and poles of f ... See full document

... We use Nevanlinna’s value distribution theory of meromorphic functions (see [1, 2]) as the main tool in the whole paper. In what follows, the growth order of w(z) is represented by σ (w) and the exponent of ... See full document

... Let w be a meromorphic function in the complex plane. The z-dependence is supposed by writing w ≡ w(z + ) and w ≡ w(z – ). We assume the reader is familiar with the stan- dard notation and results of Nevanlinna ... See full document

... a meromorphic function means meromorphic in the complex plane, and we assume the reader is familiar with the basic notions of Nevanlinna theory (see, ...the zeros of f , respectively, and we define ... See full document

... morphic solutions of the equation above, it shows that they are almost equal to each other except for a nonconstant factor, if they have the same zeros and poles counting multiplicities, when m ∈ { ... See full document

... Let w be a meromorphic function in the complex plane. The z-dependence is supposed by writing w ≡ w(z + ) and w ≡ w(z – ). We assume that the reader is familiar with the stan- dard notations and results of ... See full document

... In what follows, we use the short notation ¯ f ≡ f (z + 1) and f ≡ f (z – 1). A meromorphic solution f of a difference equation is called admissible if all the coefficients of the equation are in S(f ). ... See full document

... In this paper, a meromorphic function means being meromorphic in the whole complex plane. We also assume that the readers are familiar with the usual notations of Nevanlinna theory (see, e.g., [–]). ... See full document

... Nonlinear difference equations have long interested re- searchers in the field of mathematics as well as in other ...nonlinear difference equations from several authors ...the solutions of two ... See full document

... of meromorphic solutions of certain linear difference equations with meromorphic ...of meromorphic solutions of a nonhomogeneous linear difference ... See full document

... of meromorphic functions, we mainly study meromorphic solutions of certain types of q-difference differential equations, obtain estimates of the growth order of their meromorphic ... See full document

... a meromorphic function with order σ = σ (f ), 0 < σ < ∞ and f (z) has q zero-pole accumulation rays and p deficient values other than 0 and ∞, then p ≤ ...order meromorphic function with p zero-pole ... See full document

... An important problem related to the ARE is to find a necessary and sufficient condition for the existence of a sign definite solution of the equation. For the continuous-time system, Willems [1] derived a ... See full document

... Recently, meromorphic solutions of complex difference equations have become a sub- ject of great interest from the viewpoint of Nevanlinna theory, due to the apparent role of the existence of such ... See full document

... Lemma 3.10 see 15 . Let fz be a nonconstant meromorphic function and let Pz, f z, Qz, f z be two polynomials in fz with meromorphic coefficients small functions relative to fz. If Pz, f z and Qz, fz have no ... See full document