On the solutions of linear differential equations with singular coefficients

On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients

Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients

Let L(y) = b be a linear differential equation with coefficients in a differential field K. We discuss the problem of deciding if such an equation has a non-zero solution in K and give a decision procedure in case K is an elementary extension of the field of rational functions or is an algebraic extension of a transcendental liouvillian extension of the field of rational functions. We show how ...

A Uniqueness Result on Ordinary Differential Equations with Singular Coefficients

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the order of singularities of the coefficients and provide examples to illustrate the results. 1. Results and examples Classical results on the existence and uniqueness of ordinary differential equations are mostly concerned with continuous coeffici...

On the Growth of Solutions of Some Higher Order Linear Differential Equations With Entire Coefficients

In this paper, we investigate the order and the hyper-order of solutions of the linear differential equation

On the Growth of Solutions of Some Second Order Linear Differential Equations With Entire Coefficients

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation f ′′ +Q ( e ) f ′ + (A1e a1z +A2e 2) f = 0, where n > 2 is an integer, Aj (z) ( 6≡ 0) (j = 1, 2) are entire functions with max {σ (Aj) : j = 1, 2} < 1, Q (z) = qmz + · · · + q1z + q0 is a nonconstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove tha...