Growth of solutions of complex differential equations with entire coefficients having a multiply-connected Fatou component

Abstract

In this study, we show that all non-trivial solutions of $$f''+A(z)f'+B(z)f=0$$ have infinite order, provided that the entire coefficient A(z) has certain restrictions and B(z) has multiply-connected Fatou component. We also extend these results to higher order linear differential equations.