2021 UNC Greensboro PDE Conference.
Electron. J. Diff. Eqns., Conference 26 (2022), pp. 1-11.

Title: Lower bounds on the fundamental spectral gap with Robin boundary conditions

Authors: Mohammed Ahrami   (Univ. of Mohammed First, Morocco)
         Zakaria El Allali (Univ. of Mohammed First, Morocco)
 
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'.

Published August 25, 2022.
Math Subject Classifications: 34B05, 34L15, 34L40.
Key Words: Fundamental gap spectral; Schrodinger operators; convex potential;  Robin and Neumann boundary conditions; Airy functions.