[PDF] Top 20 Value distribution of meromorphic solutions of certain difference Painlevé III equations

... 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

... and meromorphic in the ...Nevanlinna value distribution theory (see ...the meromorphic function f (z), and λ(f ) and λ(  f ) to denote, respectively, the exponents of convergence of zeros and ... See full document

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

... a meromorphic function that is defined and meromorphic in the whole complex ...Nevanlinna value distribution and its standard symbols and notations (see ... See full document

... Halburd and Korhonen [] and Chiang and Feng [] investigated the value distribution theory of difference expressions, a key result of which is a difference analogue of the log- arithmic derivative lemma. ... See full document

... and meromorphic in z ...growth, value distribution and unicity on the meromorphic solutions to difference equations (see ... See full document

... Nevanlinna’s value distribution theory, we shall adopt the stan- dard notations associated with the theory, such as the characteristic function T (r, f ), the counting function of the poles N(r, f ), and ... 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

... 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

... : Value distribution of the difference opera- tor, Advances in Difference equations, ...and value sharing of meromorphic functions, ... See full document

... a meromorphic function always means meromorphic in the whole complex plane C, and c always means a nonzero ...Nevanlinna value distribution theory of meromorphic functions such as T(r, ... 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), ... See full document

... The difference analog of the logarithmic derivative lemma, which was obtained indepen- dently by Halburd and Korhonen [] and by Chiang and Feng [], plays a key role in the value distribution of difference ... See full document

... different value of the parameter, either for the same Painlevé equation or for ...new solutions by transformation. Specially, Painlevé equa- tion appeared in many applications and fields such as ... See full document

... In this paper, we shall adopt the standard notations in Nevanlinna’s value distribution theory of meromorphic functions. For example, the characteristic function T(r, f ), the counting function of ... See full document

... nonconstant meromorphic functions for some a ∈ C ∪ ...the value a CM (counting multiplicities), and if they coincide in locations only, we say that f (z) and g(z) share a IM (ignoring ... See full document

... A meromorphic function f (z) means meromorphic in the complex plane C . If no poles occur, then f (z) reduces to an entire function. Assume that n(r, f ) counts the number of poles of f in |z| ≤ r, each ... See full document

... The difference Nevanlinna theory and its applications to the uniqueness theory have become a subject of great interest [2-4], ...a meromorphic function f (z) sharing values with its shift f(z + c), we ... 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

... 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