Order and hyper-order of entire solutions of linear differential equations with entire coefficients

In this paper, we investigate the growth of solutions of the differential equation [GRAPHICS] where A(0)(z),..., A(k-1)(z) are entire functions with A(0)(z) not equivalent to 0. We will show that if the coefficients satisfy certain growth conditions, then every finite order solution of the equation will satisfy certain other growth conditions. We will also find conditions on the coefficients so that every solution f not equivalent to 0 will have infinite order and we estimate in one case the lower bounds of the hyper-order.