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

Lower bounds on the fundamental spectral gap with Robin boundary conditions

Mohammed Ahrami, Zakaria El Allali

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.
DOI: https://doi.org/10.58997/ejde.conf.26.a1

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Mohammed Ahrami
Team of Modeling and Scientific Computing
Department of Mathematics
Multidisciplinary Faculty of Nador
University of Mohammed First, Morocco
email: m.ahrami@ump.ac.ma
Zakaria El Allali
Team of Modeling and Scientific Computing
Department of Mathematics
Multidisciplinary Faculty of Nador
University of Mohammed First, Morocco
email: z.elallali@ump.ma

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