[PDF] Top 20 Complex oscillation of meromorphic solutions for difference Riccati equation

... the meromorphic function f (z), λ(f ), and λ(  f ) to denote the exponents of convergence of zeros and poles of f (z), ...a meromorphic function f (z) is oscillatory if f (z) has infinitely many ... See full document

... and meromorphic in the ...the meromorphic function f (z), and λ(f ) and λ(  f ) to denote the exponents of convergence of zeros and poles of f (z), ...a meromorphic function g is small with respect ... See full document

... Meromorphic solutions of complex differential equations and complex difference equations plays a prominent role in the field of Complex ...analysis. Solutions of such ... 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

... the Picard exceptional value of f n f 0 may only be zero. This conjecture has been proved by many authors. e.g., Hayman [3] proved that if f is a transcendental meromorphic function and n≥ 3,then f n f 0 takes ... 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) ... 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, ... See full document

... admissible meromorphic solution f (z), then either f satisfies a difference Riccati equation, or () can be transformed by a linear change in f to some classical difference equations, which include ... 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, ... See full document

... and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution f (z), then either f(z) is a solution of a q-difference Riccati equation ... 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

... of equation (1) is called oscillatory if for any m ∈N there exist m, m2 ≥ m such that x(m1)x(m2) <0, otherwise it is non ...oscillatory. equation (1) is called B-oscillatory if all its bounded ... See full document

... where R(z, w) is rational in w and meromorphic in z. They showed that if (.) has an admissible finite order meromorphic solution, then either w satisfies a difference Riccati equation or (.) ... See full document

... Theorem A: Let w ( z ) and u ( z ) be two nonconstant meromorphic functions. If w ( z ) and u ( z ) share 5 values IM (4 values CM, respectively) in the extended complex plane, then w z ( ) ≡ u z w z ( ) ( ... See full document

... of meromorphic functions, the growth of entire solutions and the form of transcendental meromorphic solutions of some types of systems of higher-order complex difference equations are ... See full document

... In 10 , Heittokangas et al. extended and improved the above result to higher-order difference equations of more general type. However, by inspecting the proofs in 4 , we can find a more general class of complex ... See full document

... The paper is organized as follows. In the next section, we recall basic oscillatory proper- ties of 1.1, including a quadratization formula for a certain nonlinear function which plays an important role in subsequent ... See full document

... Finally, let us consider the high order difference equation with a constant delay N(n + 1) − N (n) = aN (n) 1 − N (n − h) , (5.8) where h is a positive integer. In accordance with Corollary 3.5 and previous results ... See full document

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 463169, 11 pages doi 10 1155/2009/463169 Research Article On Boundedness of Solutions of the Difference Equation[.] ... See full document

... difference equation with constant ...characteristic equation and obtain a necessary and sufficient condition for the oscillation of all solutions of the partial difference ... See full document