On the oscillation of solutions of certain linear differential equations in the complex domain

Abstract

Our starting point is the differential equationwhere A(z) is a transcendental entire function of finite order, and we are concerned specifically with the frequency of zeros of a non-trivial solution f(z) of (1.1). Of course it is well known that such a solution f(z) is an entire function of infinite order, and using standard notation from [7],for all , b∈C\{0}, at least outside a set of r of finite measure.

Finite order solutions of second order linear differential equations

“…Even though at least one of every two linearly independent solutions of equation (1.1) See, for example, [3,4,5,6,7,8,17,21,22]. This paper is organized as follows.…”

Oscillation results on y″ + Ay = 0 in the complex domain with transcendental entire coefficients which have extremal deficiencies

“…In fact, the above theorem is a consequence of: Then, if f t and f 2 are two linearly independent solutions of (1.1), we have With some stronger hypotheses, similar results were also proved for higher order equations, we refer the readers to [4], [5] and [6].…”

On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order

“…(See [1].) Let P (z) be a polynomial of degree n 1, where P (z) = (α + βi)z n + · · ·, δ(P , θ) = α cos nθ − β sin nθ , α, β ∈ R, and let ε be a given constant, then we have …”