[PDF] Top 20 Growth of the Entire or Meromorphic Solutions of Differential-Difference Equations

... transcendental entire function has at most one Picard exceptional value, a transcendental meromorphic functions has at most two picard exceptional ... See full document

... are meromorphic functions having only finitely many poles and the poles of f can only occur at the poles of A, B and F , then f (z) must have only finitely many ...an entire function with ρ (g) = ρ (f ) ≥ ... See full document

... differential equations in the complex plane C, it is always an interesting and quite difficult problem to prove the existence or uniqueness of the entire or meromorphic solution of a given ...or ... See full document

... Thus a natural question is: what condition on B(z) will guarantee that every solution f 6≡ 0 of (1.1) will have infinite order? Frei, Ozawa, Amemiya and Langley, and Gundersen studied the question. For the case that B(z) ... See full document

... Gundersen and Yang [] proved the following well-known result which can guarantee that every solution of non-homogeneous linear differential equations has infinite order. Theorem A Let P be a nonconstant polynomial. ... See full document

... of entire solutions of order zero of a type of differential-q-difference equation, which includes equations ...all meromorphic coefficients of these monomials of growth S(r, f ... See full document

... AF: Entire solutions of f(kz) = kf (z)f ...On meromorphic solutions of certain functional ...order solutions of second order linear differential ... See full document

... transcendental entire or meromorphic ...the growth and existence of entire or meromorphic solutions of various types of non-linear differential equations, and one can find ... 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

... the growth of meromorphic solutions of some linear difference ...the growth of meromorphic solutions when most coefficients in such equations have the same order, which are ... See full document

... and meromorphic in the ...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

... a meromorphic function means meromorphic in the complex plane, and we assume the reader is familiar with the basic notions of Nevanlinna theory (see, ...of growth of f , the ex- ponent of convergence ... 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

... transcendental meromorphic solution of ...are entire functions and d(z) is the canonical product formed by all poles of f (z) such that σ (d) = λ(  f ) < μ(f ) = μ(g) ≤ σ (g) = σ (f ) < ... 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

... an entire function in the complex plane and all zeros of w (z) have multiplicity at least k (k Î N ), P[w] be a polynomial with the form ...the differential equation [Q(w (k) (z))] n = P[w], then the ... See full document

... The above theorem was derived by Hayman [] in . Later, he conjectured [] that Theorem A remains valid even if n =  or n = . Mues [] proved the result for n =  and the case n =  was proved by Bergweiler and ... See full document

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

... However, when n =  and g(z) has a specific relationship with f (z) in (.), the problem that whether we can obtain the accurate expressions of entire solutions or not is worth to be considered. Recently, ... See full document

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