Journal of Inequalities and Applications
Volume 1 (1997), Issue 4, Pages 375-400

Relative boundedness and compactness theory for second-order differential operators

Terry G. Anderson1 and Don B. Hinton2

1Department of Mathematical Sciences, Appalachian State University, Boone 28608, NC, USA
2Department of Mathematics, University of Tennessee, Knoxville, Knoxville 37996-1300, TN, USA

Received 30 January 1997

Copyright © 1997 Terry G. Anderson and Don B. Hinton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem considered is to give necessary and sufficient conditions for perturbations of a second-order ordinary differential operator to be either relatively bounded or relatively compact. Such conditions are found for three classes of operators. The conditions are expressed in terms of integral averages of the coefficients of the perturbing operator.