The hyper order and fixed points of solutions of linear differential equations

The Hyper Order and Fixed Points of Solutions of Linear Differential Equations

In this paper, we obtain a precise estimation of the hyper order of solutions for a class of higher order linear differential equation, and also investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second order case. These results generalize the results of GundersenSteinbart, Wittich and Chen-Shon. AMS Subject Classification: 30D35.

On the hyper order of solutions of a class of higher order linear differential equations

In this paper, we investigate the order and the hyper order of entire solutions of the higher order linear differential equation f +Ak−1 (z) e k−1f +...+A1 (z) e 1f ′ +A0 (z) e 0f = 0 (k ≥ 2) , where Pj (z) (j = 0, ..., k − 1) are nonconstant polynomials such that degPj = n (j = 0, ..., k − 1) and Aj (z) ( ≡ 0) (j = 0, ..., k − 1) are entire functions with ρ (Aj) < n (j = 0, ..., k − 1). Under ...

On the Hyper-order of Solutions of Second Order Linear Differential Equations with Meromorphic Coefficients

In this paper, we investigate the growth of solutions of the linear differential equation 0 = Bf f A f      , where ) (z A and 0) )( (  z B are meromorphic functions. More specifically, we estimate the lower bounded of hyperorder of solutions of the equation with respect to the conditions of ) (z A and 0) )( (  z B if solutions 0 ( f ) of the equation is of infinite order. keywords: ...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

On the hyper-order of solutions of two class of complex linear differential equations