Abstract
In 1982, Steven B. Bank and Ilpo Laine had written a paper entitled "On the oscillation theory of f" + Af = 0 where A is entire". Since then, quite a number of research articles have been concerned with the exponent of convergence of zeros and the order of the non-trivial solutions f.

One of the reasons why people are very interested in studying the above equation is because of the existence of the so-called Bank-Laine equation. Unfortunately, such equation does not seem to exist for third or even higher order differential equations. However, can we still generalize the results that were obtained in the second order case to higher order case? In this thesis, we will provide some answers to the third order case.