[PDF] Top 20 On the growth of solutions of second order complex differential equation with meromorphic coefficients
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On the growth of solutions of second order complex differential equation with meromorphic coefficients
... of meromorphic function (see [1,2]). In particular, for a meromorphic function f(z), we use the notation r(f) and μ (f) to denote its order and lower order, respectively and for a closed ... See full document
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On the growth of solutions of a class of second order complex differential equations
... are meromorphic functions, P(z) is a non-constant ...of meromorphic func- tions and the basic notions such as N(r, f ), m(r, f ), T(r, f ) and δ(r, f ... See full document
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On growth of meromorphic solutions for linear difference equations with meromorphic coefficients
... Liu Advances in Difference Equations 2013, 2013 60 http //www advancesindifferenceequations com/content/2013/1/60 R ES EA RCH Open Access On growth of meromorphic solutions for linear difference equat[.] ... See full document
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Results on the growth of meromorphic solutions of some linear difference equations with meromorphic coefficients
... the growth of meromorphic solutions of some linear difference ...the growth of meromorphic solutions when most coefficients in such equations are meromorphic functions, which ... See full document
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Growth and Complex Oscillation of Linear Differential Equations with Meromorphic Coefficients of [p,q] − ϕ Order
... their growth. In [16], in order to maintain accordance with general definitions of the entire function f of iterated p−order [13, 14], Liu-Tu- Shi gave a minor modification of the original definition ... See full document
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On hyper order of solutions of higher order linear differential equations with meromorphic coefficients
... of meromorphic functions is a powerful tool in the field of complex differential ...the complex plane by using Nevanlinna theory; see, for example ...The order of growth of ... See full document
13
8. Growth and fixed-points of meromorphic solutions of higher-order nonhomogeneous linear differential equations
... the growth and fixed points of mero- morphic solutions of higher order nonhomogeneous linear differential equations with meromorphic coefficients and their ... See full document
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On the Growth of Solutions of Some Second Order Linear Differential Equations
... Thus, a natural question is what conditions on Pz and Qz will guarantee that every solution f / ≡ 0 of 1.2 has infinite order? Ozawa 4, Gundersen 5, Amemiya and Ozawa 6, and Langley 7 have studied the problem with ... See full document
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Asymptotic Theory for a General Second Order Differential Equation
... Introduction In this paper, we examine the asymptotic form of two linearly independant solutions of the general second-order differential equation... dx The coefficients p,q and r are no[r] ... See full document
7
Properties of Solutions of Complex Differential Equations in the Unit Disc
... the complex plane and in the unit disc ∆ = {z : |z| < 1} (see [14] , [15] , [18] , [20] , ...small growth order of functions in ∆ as polynomials on the complex plane C ...small ... See full document
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Growth of meromorphic solutions of linear difference equations without dominating coefficients
... 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 ≤ ...finite order meromorphic function ... See full document
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Boundedness of solutions for a class of second-order differential equation with singularity
... where V (x, t) satisfies some growth conditions and V(x, t) = V (x, t +). The author reduced the system to a normal form and then applied Moser twist theorem to prove the existence of quasi-periodic solution and ... See full document
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Growth of the Entire or Meromorphic Solutions of Differential-Difference Equations
... the Picard exceptional value of f n f 0 may only be zero. This conjecture has been proved by many authors. e.g., Hayman [3] proved that if f is a transcendental meromorphic function and n≥ 3,then f n f 0 takes ... See full document
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On the growth of solutions of higher order complex linear differential equations
... Lemma 2.5 [4] Let "𝑓(𝑧)" be a meromorphic function of finite order“𝜌 , “and let“𝜖 > 0“be a given constant. Then there exists a set“ "𝐸 ⊆ (1, ∞)" that has finite logarithmic measure, such ... See full document
5
Subnormal Solutions of Second Order Nonhomogeneous Linear Differential Equations with Periodic Coefficients
... the solutions of a linear differential equation with periodic coefficients is one of the difficult aspects in the complex oscillation theory of differential ... See full document
12
Complex oscillation of meromorphic solutions for difference Riccati equation
... the order of growth of the meromorphic function f (z), λ(f ), and λ( f ) to denote the exponents of convergence of zeros and poles of f (z), ...a meromorphic function f (z) is oscillatory if ... See full document
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3. Growth of solutions of linear diferential equations in the unit disk
... (iterated) order of growth in the complex plane [7, 14, 15, ...all solutions of (1.1) are entire functions of finite order if and only if all coefficients are polynomials, and ... See full document
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Positive Periodic Solutions of Second Order Functional Differential Equation with Impulses
... odic solutions to the impulsive differential ...following second order nonlinear delay differential equation with periodic ... See full document
6
Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations
... 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
8
Properties of Meromorphic Solutions of a Class of Second Order Linear Differential Equations
... In 2002, Chen [3] considered the question: What conditions on B(z) when ρ(B) = 1 will guarantee that every nontrivial solution of (1.1) has infinite order? He proved the following result, which improved results of ... See full document
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