Journal of Inequalities and Applications
Volume 5 (2000), Issue 4, Pages 321-342

A computational investigation of an integro-differential inequality with periodic potential

B. M. Brown1 and V. G. Kirby2

1Department of Computer Science, Cardiff University, P.O. Box 916, Cardiff CF3 3XF, UK
2School of Mathematics, Kingston University, Penrhyn Road, Kingston Upon Thames, Surrey KT1 2EE, UK

Received 16 April 1999; Revised 12 July 1999

Copyright © 2000 B. M. Brown and V. G. Kirby. 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.


This paper is concerned with a certain integral inequality whose associated differential expression contains a periodic potential. In these problems the spectrum consists of bands which may have eigenvalues in the gaps. We use numerical methods to estimate the location of these bands and position of the eigenvalues and use this information to produce new examples of the HELP inequality.