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

Abstract

For a second order linear differential equation $f^{\prime \prime }+A(z)f^{\prime }+B(z)f=0$, 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.

arXiv comment14 page. Comments are welcome