[PDF] Top 20 On properties of meromorphic solutions for difference Painlevé equations

... difference Painlevé I and II equations from difference equation ...admissible meromorphic solution f (z), then either f satisfies a difference Riccati equation, or () can be transformed by a linear ... See full document

... 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 (see [13] , [20]). In ... 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

... 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

... 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

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

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

... admissible meromorphic solution of finite order, then either ω satisfies a difference Riccati equation, or equation ...difference Painlevé equation or a linear difference ...of properties of difference ... See full document

... the properties of meromorphic solutions of Painlevé III difference ...rational solutions of the equation assume only one form and the transcendental solutions have at most one ... See full document

... [19-23], difference inequalities [24-28], Volterra- Fredholm type inequalities [24,27], and dynamic inequal- ities on time scales ...quantitative properties of solutions of certain fractional d- ... See full document

... a meromorphic function f (z), we denote by T (r, f ), N(r, f ) the characteristic function and the counting function of f (z), ...a meromorphic function f (z) ... See full document

... Entire solutions of f(kz) = kf (z)f ...On meromorphic solutions of certain functional ...order solutions of second order linear differential ... See full document

... entire solutions of order zero of a type of differential-q-difference equation, which includes equations ...all meromorphic coefficients of these monomials of growth S(r, f ... See full document

... In this paper, we use the basic notions of Nevanlinna theory [1–4] such as the character- istic function T(r, f ), counting function N(r, f ), and proximity function m(r, f ). We also use S(r, f ) to denote any quantity ... See full document

... In this paper, we use the basic notions in Nevanlinna theory of meromorphic functions, as found in []. In addition, we use δ(f ), λ(f ), and λ(  f ) to denote the order, and the exponents of the convergence of ... See full document

... for difference equations of entire functions of small ...the difference analogue of logarithmic derivative f(z+c) f(z) were given by Halburd and Korhonen [1] ...differential equations are ... See full document

... 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

... 9. Liu, K., Liu, X., Cao, T.B. : Value distribution of the difference opera- tor, Advances in Difference equations, Vol.2011, Art ID 234215,12 pages. 10. Yang, C.C., Hua, X.H.: Uniqueness and value ... See full document

... and meromorphic in z with slow growth ...admissible meromorphic solution of finite order, then either w satisfies a difference Riccati equation or ...difference equations include Painlevé I, II ... See full document

... transcendental meromorphic solutions to some nonlinear difference ...transcendental meromorphic so- lutions to some nonlinear difference equations of the form ... See full document