[PDF] Top 20 Existence of zero order meromorphic solutions of certain q difference equations

... 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

... It is well known that f (z) = f (z + c) – f (z) is regarded as the difference counterpart of f . Thus a natural question is: Can we change the above second-order linear differen- tial equation to the linear ... See full document

... finite order transcendental mero- 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 ... See full document

... It becomes natural for us to ask the following question: Does the conclusion of Theo- rem 1.1 remains valid if the condition “u is a non-zero rational function and v is a non- constant polynomial” is replaced by a ... 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

... the existence of admissible meromorphic solutions of systems of complex difference equation ...the order of entire solutions of systems of complex difference equation ...transcendental ... See full document

... investigate meromorphic solutions of linear difference equations and prove a number of ...of meromorphic solutions under some special cases and provide some examples to show that the ... 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 ... See full document

... and meromorphic in the ...the order of growth of 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

... 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 ... 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

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

... The q-difference equations initiated at the beginning of the twentieth century [–] is a very interesting field in difference ...nonlinear q-difference equations is still in the initial stages ... 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

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

... a meromorphic function means being meromorphic in the whole complex ...the order and the lower order of a meromorphic function f ... See full document

... a meromorphic function a(z)is called a small function with respect to f if and only if T[r, a (z)] = o(T(r, f)) as r tends to infinity outside of a possible exceptional set of finite logarithimic ... See full document

... Remark . From the proof of Theorem ., we see that the restriction in Theorem . to p, q, and R may extend to small functions. In fact, it is easy to find that the conclusion is valid provided that p, q, ... See full document

... Remark . In Theorem ., we presented an existence result for weak solutions of the problem (.) in the case where the Banach space E is reflexive. However, in the nonre- flexive case, conditions (H)-(H) ... See full document

... the solutions of boundary value problems (1.1) with (1.2) for a second-order p-Laplacian difference equation ...the existence and multiple results are ... See full document