Lower order and Baker wandering domains of solutions to differential equations with coefficients of exponential growth

We investigate transcendental entire solutions of complex differential equations f ″ + A ( z ) f = H ( z ) , where the entire function A ( z ) has a growth property similar to the exponential functions, and H ( z ) is an entire function of order less than that of A ( z ) . We first prove that the lower order of the entire solution to the equation is infinity. By using our result on the lower order, we prove the entire solution does not bear any Baker wandering domains.