[PDF] Top 20 All meromorphic solutions of some algebraic differential equations and their applications

... For details on Nevanlinna’s value distribution theory, please see []. We denote by S(r, f ) any function satisfying S(r, f ) = o { T (r, f ) } , as r → ∞ , possibly outside of a set of finite measure. We say that a ... 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

... such equations could possess analytic solutions of infinite order in the unit disk, but obtained a uniform growth estimate for all such ...arbitrary meromorphic solutions in the disk, no ... 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 ... See full document

... Yan qing et al Advances in Difference Equations 2014, 2014 52 http //www advancesindifferenceequations com/content/2014/1/52 R ES EARCH Open Access Global homeomorphism and applications to the existen[.] ... See full document

... Theorem 1.2 Under the assumptions of Theorem 1.1, let ϕ (z) 6≡ 0 be a meromor- phic function with finite iterated p−order in ∆ such that ψ (z) is not a solution of (1.1) . If f (z) is an infinite iterated p−order ... See full document

... Using the different and much simpler proofs, this paper provides two main results on Ω (α, β), which extend the main results that were derived in [1]. To bring about our results from the more general hypotheses without ... See full document

... of meromorphic solutions and their derivatives of higher-order nonhomogeneous linear differential equations with meromorphic ...generalized some previous results that are related to ... See full document

... 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 [H(w(z))] n = P[w], then the growth order l := l (w) of w(z) ... See full document

... of meromorphic functions (see [21, 25]). The term “meromorphic function” will mean meromorphic in the whole complex plane C ...a meromorphic function f (z), λ(f ) to denote the exponents of ... See full document

... ON THE CARDINALITY OF SOLUTIONS OF MULTILINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS.. ARGYROS Department of Mathematics University of Iowa Iowa City, Iowa 5222 U.S.A..[r] ... See full document

... Remark . From [], Remark ., we know that the condition that the multiplicity of poles of the meromorphic solution f is uniformly bounded is necessary. Hence the condi- tion was missing in Theorems . and ... See full document

... Entire solutions of f(kz) = kf (z)f ...R: Some results on factorization of meromorphic ...On meromorphic solutions of certain functional ...order solutions of second order linear ... See full document

... transcendental meromorphic solution of ...by all poles of f (z) such that σ (d) = λ(  f ) < μ(f ) = μ(g) ≤ σ (g) = σ (f ) < ...for all z satisfying |z| = r ∈ / [, ] ∪ E  ∪ E  and |g(z)| = ... See full document

... of meromorphic func- tions (see [–]). The term ‘meromorphic function’ will mean meromorphic in the whole complex plane ...a meromorphic function f (z), λ(f ) to denote the exponents of ... See full document

... of meromorphic solutions of some second order linear differential equations, where it is assumed that the coefficients are meromorphic ... 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 ...of all ... 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 vali[r] ... See full document

... Theorem A: Let w ( z ) and u ( z ) be two nonconstant meromorphic functions. If w ( z ) and u ( z ) share 5 values IM (4 values CM, respectively) in the extended complex plane, then w z ( ) ≡ u z w z ( ) ( ) ( = T ... See full document

... g., [13] and the references in [11,18]-Added in proof). However, the latter condition is strong and rather hard to verify in practice, though some examples and general criteria for this convergence are known (see, ... See full document