[PDF] Top 20 Existence and properties of meromorphic solutions of some q difference equations

... A meromorphic function α(z) is called a small function with respect to f (z), if T(r, α) = S(r, f ), where S(r, f ) denotes any quantity satisfying S(r, f ) = o(T (r, f )) as r → ∞ outside a possible exceptional ... 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

... the existence and the growth of tran- scendental meromorphic solutions of complex q-difference equations ...differential- q-difference equations) instead of complex difference ... See full document

... fractional q-difference calculus had its origin in the works by Al-Salam [] and Agarwal ...fractional q-difference calculus were made, for example, q-analogues of the integral and differential ... 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 ... See full document

... difference equations, difference products and q-differences in the complex plane C , and a number of papers (including [–]) have focused on the value distribution and uniqueness of differences and differences ... See full document

... fractional q-difference equations have aroused considerable ...the existence and multiplicity of solutions or positive solutions for boundary value problems of nonlinear ... See full document

... on meromorphic solutions of complex functional equations (see ...on q-difference ...of meromorphic solutions of q-difference equations and obtained results which ... 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 ... 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

... differential equations with nonlocal conditions in Banach space, [15] ...the existence and uniqueness of the solutions to the nonlocal problem for the fractional differential equation in Banach ... See full document

... The existence and uniqueness of solutions for the problem are proved by means of the Leray-Schauder nonlinear alternative and some standard fixed point ...D q u(t) in the ... 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

... morphic solutions of (.), from which a q-difference analogue of the classical Malmquist theorem [] is given: if the q-difference equation ...a meromorphic solution of order zero, then (.) ... See full document

... and Q(z) are non-constant polynomials, by Theorem D, we see that ...entire solutions of finite order. If m = n ≥ , rewriting (.) as Q(z)  (f (z)) n + Q(z) P(z) f m (z + c) = , by Theorem ... 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

... A meromorphic solution w of a difference equation is called admissible if all coefficients of the equation are in ...non-rational meromorphic solutions are admissible; if an admissible solution is ... See full document

... 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

... 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

... 10. Jackson, FH: On q-functions and a certain difference operator. Trans. R. Soc. Edinb. 46, 253-281 (1908) 11. Bird, MT: On generalizations of sum formulas of the Euler-Maclaurin type. Am. J. Math. 58, 487-503 ... See full document