Decay of solutions of ordinary differential equations

We investigate the rate of decay of eigenfunctions of Schrodinger equations using a perturbation method which consists of making a perturbation B of the operator L of the form B[y] = L[y] - (g(-1)Lg)[y], where g is an appropriately chosen function. In our theory we allow B to be either relatively compact or satisfy a certain boundedness condition. We give some examples which apply the results of our main theorems coupled with recent work on the relative boundedness and compactness of differential operators. (C) 2002 Elsevier Science (USA). All rights reserved.