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

Abstract

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.

Keywords

• Integral inequality
• Ordinary differential equations
• Titchmarsh&#8211;Weyl <it>m</it>-function
• Periodic potential
• Numerical methods