Lower bounds on the fundamental spectral gap with Robin boundary conditions

Abstract

This article investigates the gap between the first two eigenvalues of Schrodinger operators on an interval subjected to the Robin and Neumann boundary conditions for a class of linear convex potentials. Furthermore, when the potential is constant the gap is minimized. Meanwhile, we establish a link between the  first eigenvalues and the real roots of the first derivative of the Airy functions Ai' and Bi'. For more information see https://ejde.math.txstate.edu/conf-proc/26/a1/abstr.html