[PDF] Top 20 Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations
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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
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Properties of Meromorphic Solutions of a Class of Second Order Linear Differential Equations
... In this paper, we shall assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions (see [13] , [20]). In ... See full document
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Growth and Complex Oscillation of Linear Differential Equations with Meromorphic Coefficients of [p,q] − ϕ Order
... ϕ order of meromorphic functions in the complex plane to study the growth and zeros of second order linear differential ... See full document
17
Some results of meromorphic solutions of second order linear differential equations
... of meromorphic func- tions (see [–]). The term ‘meromorphic function’ will mean meromorphic in the whole complex plane ...the order of growth of a meromorphic function f (z), ... See full document
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Growth of the Entire or Meromorphic Solutions of Differential-Difference Equations
... A finite value a is called the Picard exceptional value of f, if f - a has no zeros. The Picard theorem shows that a transcendental entire function has at most one Picard exceptional value, a transcendental ... See full document
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8. Growth and fixed-points of meromorphic solutions of higher-order nonhomogeneous linear differential equations
... transcendental meromorphic functions(see ...of solutions of the general differential ...of solutions of second order linear differential equations with ... See full document
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Growth and fixed points of meromorphic solutions of nonhomogeneous linear differential equations
... of meromorphic func- tions (see [–]). The term ‘meromorphic function’ will mean meromorphic in the whole complex plane C ...the order of growth of a meromorphic function f (z), ... See full document
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On the growth of solutions of certain higher order linear differential equations
... Lemma . ([]) Let f (z) be a transcendental meromorphic function, and let α > be a given constant. Then there exist a set H ⊂ (, ∞) that has a finite logarithmic measure and a constant B > depending ... See full document
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Results on the growth of meromorphic solutions of some linear difference equations with meromorphic coefficients
... above second-order linear differen- tial equation to the linear difference equation? What conditions will guarantee that every meromorphic solution will have infinite order when ... See full document
13
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
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On the growth of solutions of a class of second order complex differential equations
... To state our theorem, we give some remarks first. Let P(z) = (α + iβ)z n + · · · (α, β ∈ R) be a non-constant polynomial. Denote δ(P, θ ) = α cosnθ – β sin nθ , let deg P be the degree of P(z), (θ , ε, r) = {z : θ – ε ... See full document
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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
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A program for predicting the intervals of oscillations in the solutions of ordinary second order linear homogeneous differential equations
... particular solutions of this equation, sin(t) and cos(t), are not necessarily oscillatory because t ∝ sin – ...the solutions of equation ...The solutions of equation (), the Chebyshev polynomials, ... See full document
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Growth of meromorphic solutions of certain types of q difference differential equations
... of meromorphic functions, we mainly study meromorphic solutions of certain types of q-difference differential equations, obtain estimates of the growth order of their ... See full document
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A powerful diagnostic tool of analytic solutions of ordinary second order linear homogeneous differential equations
... first-order equations for verification ...of solutions of equation () using a new technique that we describe in Appendix ...The second predictor takes an analytically tractable form in the ... 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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On decreasing solutions of second order nearly linear differential equations
... Remark A closer examination of the proof of Theorem shows that the condition lim u→+ | ˆ F(u)| = ∞ is somehow needed. Indeed, if we assume that this limit is finite and that a ∞ H(s) ds = ∞, then in view of () we ... See full document
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On hyper order of solutions of higher order linear differential equations with meromorphic coefficients
... 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
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Properties of Solutions of Complex Differential Equations in the Unit Disc
... of differential polynomial generated by meromorphic and analytic solutions of second order linear differential equations with meromorphic coefficients and ... See full document
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3. Growth of solutions of linear diferential equations in the unit disk
... infinite order? Many authors have investigated the growth of the solutions of complex linear differential equations in C , see [2, 3, 4, 5, 6, 10, 15, 21, 22, 28, ... See full document
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