[PDF] Top 20 Meromorphic Solutions of Some Complex Difference Equations

... 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

... Meromorphic solutions of complex differential equations and complex difference equations plays a prominent role in the field of Complex ...analysis. ... See full document

... the complex difference equations have been got ...of meromorphic solutions of some difference equations, and several papers [, , –] deal with analytic properties 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 ... See full document

... greater than the others. Then, for any meromorphic solution of Eq. (1), we have σ (f ) ≥ σ + 1. The condition about type in Theorem D still means the growth of some coefficient is faster than the others, ... See full document

... Entire solutions of f(kz) = kf (z)f ...R: Some results on factorization of meromorphic ...On meromorphic solutions of certain functional ...order solutions of second order linear ... See full document

... and meromorphic in z with slow growth ...admissible meromorphic solutions of finite order, then either w satisfies a difference Riccati equation, or ...difference equations, which contains many ... See full document

... Remark . It is unlikely that most of the q-difference equations studied in this paper have meromorphic solutions due to the properties of the q-difference operator. The reason for this is the ... See full document

... and meromorphic in ...zero-order meromorphic solution f (z), then either f(z) is a solution of a q-difference Riccati equation or the coefficients satisfy some ... See full document

... were some paper focusing on the properties of solutions of some systems of complex difference equations and q-shift difference equation (see [, , ... See full document

... of meromorphic functions will be used (see Hayman [], Yang [] and Yi and Yang ...a meromorphic function f (z), we also use S(r, f ) to denote any quantity satisfying S(r, f ) = o(T (r, f )) for all r ... See full document

... of meromorphic so- lutions of some systems of complex difference equations and obtained some existence theorems and estimates on the proximity function and the counting function of ... See full document

... on complex difference equa- tions and difference analogs of Nevanlinna’s ...the complex difference equations have been got ...of meromorphic solutions of difference ... See full document

... of meromorphic func- tions (see [–]). The term ‘meromorphic function’ will mean meromorphic in the whole complex plane ...a meromorphic function f (z), λ(f ) to denote the exponents ... See full document

... of meromorphic solutions of some algebraic differential ...all meromorphic solutions of certain algebraic differential equations with constant coefficients and dominant ...the ... See full document

... Recently, with the development of Nevanlinna value distribution theory on difference expressions [–], Halburd and Korhonen [] gave the full classification of the family in- cluding Painlevé I and II difference ... See full document

... admissible meromorphic solution of finite order, then either w satisfies a difference Riccati equation or equation ...difference equations. These simple difference equations include Painlevé I, II ... See full document

... a meromorphic function always means meromorphic in the whole complex plane C, and c always means a nonzero ...of meromorphic functions such as T(r, f ), m(r, f ) and N(r, f ) as explained in ... 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

... For the q-difference equation (.), Theorem C only considered the case when solutions have Borel exceptional zeros and poles. But how about the existence and growth of mero- morphic solutions of (.)? ... See full document