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

... and meromorphic solutions of complex difference equations owing to the introduction of Nevanlinna theory in this ...complex q-differences and q-difference equations is an important ... See full document

... the existence and growth of meromorphic solutions of differ- ence equations have been investigated in many papers ...the q-difference analog of Nevanlinna theory, there has been a ... 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 ... 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

... the existence and growth of solutions of complex differ- ence equations will be ...of meromorphic functions will be used in this paper (see ...a meromorphic function f , S(r, f ) ... 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 ...The nonlinear team f contains D ... See full document

... a meromorphic function with order σ = σ (f ), 0 < σ < ∞ and f (z) has q zero-pole accumulation rays and p deficient values other than 0 and ∞, then p ≤ ...= q ≥ 1, and the set of such f (z) is ... See full document

... Fractional differential calculus is a discipline to which many researchers are dedicating their time, perhaps because of its demonstrated applications in various fields of science and engineering []. Many researchers ... See full document

... about q-difference calculus or quantum calculus were first developed by Jackson [, ], while basic definitions and properties can be found in the monograph by Kac and Cheung ...[]. q-Difference ... 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

... 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

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

... of nonlinear fractional q-difference equations with parameter involving the Riemann-Liouville fractional ...cones, some positive solutions are obtained. As applications, some ... See full document

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

... we similarly obtain that d ≤ n. This completes the proof of Theorem .. Proof of Theorem . If f (z) is a transcendental meromorphic solution of (.), then by the Valiron-Mohon’ko identity ([], Theorem ... See full document

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

... and meromorphic in ...zero-order meromorphic solution f (z), then either f(z) is a solution of a q-difference Riccati equation or the coefficients satisfy some ... See full document

... of meromorphic functions will be used (see Hayman [], Yang [] and Yi and Yang ...a meromorphic function f (z), we also use S(r, f ) to denote any quantity satisfying S(r, f ) = o(T (r, f )) for all r ... 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 [–]. The ... See full document

... a nonlinear equation to a linear one. If the transformed equations are with constant coefficients, then they are solvable (see [4–7, 10, 11, 13]), which implies the solvability of the original ...by ... See full document