On Zeros and Growth of Solutions of Second Order Linear Differential Equations

TL;DR

This paper proves that solutions to certain second order linear differential equations with transcendental entire coefficients are of infinite order and have infinitely many zeros, extending the results to higher order equations.

Contribution

It establishes that solutions to these differential equations are of infinite order and possess infinitely many zeros, generalizing previous results to higher order equations.

Findings

Solutions are of infinite order

Solutions have infinitely many zeros

Results extended to higher order equations

Abstract

For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restriction, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions have infinite number of zeros. Also, we have extended these results to higher order linear differential equations.