[PDF] Top 20 Growth of meromorphic solutions of certain types of q difference differential equations

... In this paper, we assume that the reader is familiar with the standard symbols and fun- damental results of Nevanlinna theory []. In addition, we use notations λ(  f ) and ρ(f ) to denote the exponent of convergence of ... See full document

... on meromorphic solutions of complex functional equations (see ...on q-difference ...the growth of meromorphic solutions of q-difference equations and obtained ... See full document

... On transcendental meromorphic solutions of certain type of nonlinear algebraic differential equations Zhang Advances in Difference Equations (2016) 2016 300 DOI 10 1186/s13662 016 1030 0 R E S E A R C[.] ... See full document

... follows, Q(r, f ) is such a quantity that if the order ρ(f ) < ∞ , then Q(r, f ) = O(1), as r → ∞ ; if the order ρ(f ) = ∞ , then Q(r, f ) = ... See full document

... of meromorphic functions (see [1, 2]) as the main tool in the whole ...the growth order of w(z) is represented by σ (w) and the exponent of convergence of the zeros and poles of w(z) are represented by λ(w) ... See full document

... two types of complex q-shift difference equations with meromorphic solutions from the point of view of Nevanlinna ...of solutions of the system of complex difference ... 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 difference ... See full document

... In this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna theory (e.g., see [–]). In addition, we will use the notation σ (f ) to denote the order of ... See full document

... Remark . By some further analysis on the proof of Theorem . in [], we can obtain the conclusion of Lemma . when P(z, f ) is a differential-difference polynomial in f . Lemma . ([]) Assume that c is a nonzero ... See full document

... investigate solutions of higher-order complex q-difference ...of growth and value distribution of meromorphic solutions of differential ...linear q-difference equations, ... See full document

... ), Q(z) ( ≡ ) be meromor- phic functions that have finitely many poles and max { ρ(R), ρ(Q)} < deg(P) = n and k be a positive ...every meromorphic solution f ≡  of equation ... See full document

... The above theorems deal with the case that the coefficients of Eq. (1) are polynomials, and there exists a dominating coefficient. Then a natural question arises: can we estimate the growth of the Eq. (1) provided the ... 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 some examples to ... 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

... 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

... 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

... In this paper, a meromorphic function means being meromorphic in the whole complex plane. We also assume that the readers are familiar with the usual notations of Nevanlinna theory (see, e.g., [–]). ... 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

... 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 renewed interest in ... See full document

... of meromorphic functions (see [11], [14], ...a meromorphic function f in the complex plane C , we will use the notations λ (f ) and λ (f ) to denote respectively the exponent of convergence of the zeros and ... See full document