Growth and Oscillation Theory of [P,Q]-Order Analytic Solutions of Linear Differential Equations in the Unit Disc (original) (raw)

Oscillation of fast growing solutions of linear differential equations in the unit disc

Acta Universitatis Sapientiae Mathematica, 2010

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f (k) + A (z) f = 0, k ≥ 2, where A (z) ≡ 0 is an analytic function with finite iterated porder and analytic functions of finite iterated p-order in the unit disc ∆ = {z ∈ C : |z| < 1}. Instead of looking at the zeros of f (j) (z) − z (j = 0, .., k) , we proceed to a slight generalization by considering zeros of f (j) (z) − ϕ (z) (j = 0, .., k), where ϕ is a small analytic function relative to f such that ϕ (k−j) (z) ≡ 0 (j = 0, ..., k), while the solution f is of infinite iterated p-order. This paper improves some very recent results of T. B. Cao and G. Zhang, A. Chen.

GROWTH AND OSCILLATION OF DIFFERENTIAL POLYNOMIALS IN THE UNIT DISC

In this article, we give sufficiently conditions for the solutions and the differential polynomials generated by second-order differential equations to have the same properties of growth and oscillation. Also answer to the question posed by Cao [6] for the second-order linear differential equations in the unit disc.

Second order complex differential equations with analytic coefficients in the unit disc

Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics, 2018

In this article, we investigate the growth of solutions of second order complex differential equations in which the coefficients are analytic in the unit disc with lower [p, q]-order. We've proved similar results as in the case of complex differential equations in the whole complex plane with usual [p, q]-order. We define also new type of order applied on the coefficients to study the growth of solutions.

Growth and oscillation theory of solutions of some linear differential equations

Matematicki Vesnik, 2008

The basic idea of this paper is to consider fixed points of solutions of the differential equation f (k) + A (z) f = 0, k ≥ 2, where A (z) is a transcendental meromorphic function with ρ (A) = ρ > 0. Instead of looking at the zeros of f (z) − z, we proceed to a slight generalization by considering zeros of f (z) − ϕ (z), where ϕ is a meromorphic function of finite order, while the solution of respective differential equation is of infinite order.