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Differential Polynomials Generated by Second Order Linear Differential Equations
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B. Belaïdi
Published/Copyright:
June 9, 2010
Abstract
In this paper, we study fixed points of solutions of the differential equation
ƒ″ + A1 (z) ƒ′ + A0 (z) ƒ = 0,
where Aj (z) (≢ 0) (j = 0, 1) are transcendental meromorphic functions with finite order. Instead of looking at the zeros of ƒ (z) – z, we proceed to a slight generalization by considering zeros of g (z) – φ(z), where g is a differential polynomial in ƒ with polynomial coefficients, φ is a small meromorphic function relative to ƒ, while the solution ƒ is of infinite order.
Key words and phrases.: Linear differential equations; meromorphic solutions; hyper order; exponent of convergence of the sequence of distinct zeros; hyper exponent of convergence of the sequence of distinct zeros
Received: 2007-12-05
Revised: 2008-07-14
Published Online: 2010-06-09
Published in Print: 2008-December
© Heldermann Verlag
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Articles in the same Issue
- Functions Preserving Some Types of Series
- On the Lipschitz Continuity of the Solutions of a Class of Elliptic Free Boundary Problems
- Distortion and Convolutional Theorems for Operators of Generalized Fractional Calculus Involving Wright Function
- Some New Generalizations of Critical Point Theorems for Locally Lipschitz Functions
- Stability of Impulsive Hybrid Set-Valued Differential Equations with Delay by Perturbing Lyapunov Functions
- Existence of Pareto Equilibria for Non-Compact Constrained Multi-Criteria Games
- Uniform Algebras in the Cantor and Baire Spaces
- Bounded Controllers for Uncertain Nonlinear Systems
- On a Refinement Type Equation
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- Existence Results of l-Point BVP for Higher Order Differential Equations with One-Dimension p-Laplacian
- Erratum to the Paper “Sufficiency and Duality in Control Problems with Generalized Invexity”
